Yes at best, maybe at worst.
So, before we begin, despite not a lot let's leave it clear what exactly must be achieved here:
the animal must be scientifically possible.
the animal must be able to be at least 15 feet long and ideally 20 feet long (or from 4,5 to 6 meters long)
it must be able to fly.
it would ideally have 6 limbs.
ideally it'd also be somewhat built for predation, because dragons.
With that done and using an earth-like planet for lyria, we can safely say that... Without the 3rd pair, your dragon is not only completely possible, but has actually existed, and it was called Hatzegopteryx thambema.
Art by RickCharlesOfficial
Hatzegopteryx as is fits 5 out of our 6 criteria. This azhdarchid pterosaur, as far as we know, could grow to a height of about 18 feet tall (or about 5,4 meters tall), and had a wingspan between 35 and 40 feet. While shorter than its close relatives, it's shorter neck, along with its sturdier Jaws, were most likely some of the adaptations necessary for its role in hateg Island: due to the lack of large Theropod dinosaurs in the island, hatzegopteryx was capable of filling in the niche, capable of taking down creatures larger than bite-sized (which here roughly means about human sized), something not exactly common in the group it belonged to. As a result, it became one of the largest apex predators to ever fly. As a cherry on the top, despite being quite adapted to spend long periods on the ground, we expect these creatures to have been easily capable of crossing continents, being anything but bad at flying.
So even in a worst case scenario where your dragon wouldn't be able to have 6 limbs, it could still very much exist, grow to be the desired size (although it'd come more from a long neck than a long tail, resulting in something a little shorter than your average giraffe) and be more than capable of filling a role as a large predatory animal, potentially even top predator depending on what it's competing against.
And so we come to the issue: the 3rd pair. Hatzegopteryx belongs to the azhdarchid family, a group that includes most of the largest flying animals known to us, said animals being likely close to the absolute limit a flying creature could grow to be. There's also another problem: "useful" mass. One big difference between birds and pterosaurs is that, while pterosaurs were quadrupedal and used both their wing limbs and hind limbs to move on the ground, birds are bipedal and adapted their front and hind limbs for flying and walking and/or climbing respectively. This may not seem like much, but it was a huge boom for pterosaurs: birds need strong hind legs to move on the ground, but once they take off those heavy, muscular legs become little more than a dead weight, like the wheels on a plane. Meanwhile, pterosaurs could still make use of the muscles in their wing limbs in both types of locomotion. This meant that, while larger birds had to distribute the muscle weight between the arms and legs, pterosaurs could maintain their leg muscles to a minimum while concentrating most of their muscle mass on their wing limbs, which contributed to their ability to reach larger sizes.
The minor problem with this neat approach is that it essentially leaves little to no room to turning it into a hexapod, because such a creature needs to keep its weight to a minimum, and our prime example was already fully developed as to not require another pair of limbs, and chances are that making it so it used the new pair to move instead of the wings would result in the bird problem.
I can't say for sure that it would be impossible, in fact, I'd say it likely isn't, but chances are that the last pair would have very litle purpose, being reduced and relatively weak or reduced at best and atrophied at worst. Your dragon would likely still be possible, especially at the lower height of 15 feet, and would probably look more or less like either of the following:
The reduced pair would most likely be tied to something such as mating displays as a sign of health on the adult (since being able to maintain these mostly useless limbs, like peacock feathers and deer antlers, requires one to be fairly capable at surviving and healthy. There's even a chance they'd have more vibrant colors than the rest of the body for display reasons), otherwise playing little purpose other than maybe help keeping the female in place during courtship and minor use for holding onto food, depending on their arrangement and length. In a worst case scenario, they could likely still reach the desired length from beak to the tip of their legs on the lower size estimates.
Edit: Or maybe not so much...
The answer above was mostly based on a more free interpretation of a dragon as "a flying animal that's usually also a carnivore", which allowed me to use some of our own planet's prime examples. The more classic dragon aesthetic you later started to want however has a lot of problems, most of which go directly against the direction we want to go for a more plausible animal and can't always be justified in the best way. Let's look at the main offenders:
the horns. Their heads being adorned with horns or horn-like structures is not necessarily impossible, far from it as we see in certain bird and pterosaur species, but a realistic dragon would have horns with an internal structure much like the bills of toucans or hornbills, being relatively sturdy and deceptively light, and probably used for purposes such as mating displays, thermoregulation, or both. However, they'd be far less durable than those of moose and ruminants, since they need to be spongy to be light. Coupled with that, having more than one or two large horns would start to be a problem in this specific case, because we're working with a creature that must still fly without sacrificing size, meaning we're on a fairly tight weight budget. Not the main offender, but still something relevant simply because of the size of the animal.
the front limbs. Again, as I said before, leaving the wings exclusively for flying isn't impossible, but it takes a heavy toll on how big your creature can be. Having them use their hind limbs and wings to walk instead of the 4 limbs is more or less a must if we want them to grow big. Ideally the front limbs would be essentially atrophied to minimize their weight, but having weaker, more dexterous limbs shouldn't be too bad.
the tail. Oh, the tail, such a lovely Trait but such a problem. Long tails by default tend to be dead weight for flying animals, as they can rarely provide enough lift or maneuverability to justify their weight and maintenance costs. Even worse: essentially all examples of flying vertebrates (at least human sized) known, unless I'm missing something, had tails that were short at best and absent at worst, and the smaller ones weren't much better, usually having tails that functioned more like thin, rigid bony rods than the classic serpentine tails we usually see in classic dragon depictions. The simplest alternative I can think of to at least keep the illusion of a long tail is to go for the bird approach and make your dragon feathered, giving them a stumpy, feathered tail containing some elongated feathers (but not necessarily all of them), offering some extra lift while keeping the added weight to a miminum. This isn't exactly impossible, as feathers are fairly old and pterosaurs, in a worse case scenario, were actually covered in feather-like growths like those of the ancestors of feathered animals.
the teeth. Nope. If long tails are already rare in larger fliers, you essentially won't find true teeth in anything that was human sized or larger. Teeth overall are not only problematic to grow, meaning more time in the egg, they're also heavier than a beak, which in our case makes it one of the first things to be sent away. Don't worry though, beaks can still be useful, and if you really want teeth, things like the hooked beaks of raptors or the jagged beak of pelagornis aren't impossible, especially if your dragon is carnivorous and has a diet of mostly fish.
So factoring those into account, a large creature that's still mostly similar to a dragon while trying to put in practice the needed traits to remain light and thus grow big would probably be a little closer to the following rough sketch, with horns in blue and tail feather length in orange:
Not a hatzegopteryx with a pair of arms slapped in anymore, but still far from the classic dragon design. The front pair of limbs would be nearly guaranteed to be the weakest overall, likely ranging from atrophied to T-Rex esque (not exactly weak, but proportionately very small) to weak and mostly useful for manipulation of tools and handling food. Their middle and hind pairs would still follow a more pterosaur-like design, with the wing limbs doing most of the muscle work as to better reduce the amount of "useless" mass when they take off. The actual tail would still need to be small, since at such sizes a longer tail is guaranteed to be too big of an encumbrance, but the feathers on it help give the illusion of a longer and bendier tail at a fraction of the weight.
So summing it all up: sorry, but as far as we're aware a more azhdarchid-like bodyplan is the best option on the market for a plausible large carnivorous flier, and there's only so much we can stray from that design without having to eventually start to sacrifice size (unfortunately, Dragons are usually very bulky, very large and very good at flying, but in the real world these are traits that pull in opposing directions, and often only be implemented 2 at a time).
Not all hope is lost though. Dragons with a more classic look can still be a part of your world without being unrealistic, only problem being they can't really reach the sizes you want. As a matter of fact, smaller pterosaurs are frighteningly similar to most Wyvern depictions. A good example of this is Harpactoganthus gentryii, a pterosaur that was about the size of a dog, but that is known to have had teeth, a noticeable head crest and a long (although mostly rigid) tail, being an extra pair of limbs and some extra minor tweaks away from being a near perfect match for a downscaled version of your ideal dragon design.
fArt by paleosir*
Edit 2: ...Unless we use the T-rex approach.
Apart from this, there's only one potential way to technically meet all of the criteria: not meeting them simultaneously, or the T-rex approach. One thing that's not exactly unheard of in nature is a difference in niche not only between species, but also within the same species: many arthropods that undergo full metamorphosis have grounded larva phases and winged adult ones (sometimes with each having a completely different type of diet), and while vertebrates don't demonstrate such drastic changes, T-rex is a great example of what we want: adult T-rexes were stronger, but fairly slow and built to overpower large prey, most likely filling the niche of large sized ambush predator in its habitat. Meanwhile, juvenile T-rexes, while smaller and weaker, were much nimbler and capable of reaching much higher speeds than their adult counterparts, allowing them to fill in the niche of mid-sized pursuit predator along with other theropods such as dakotaraptor. Essentially, due to the changes they undergone as they matured and the sheer size difference between the fully grown adults and the babies and juveniles, T-rexes occupied different niches throughout their lives.
Your dragons could have a very similar, although potentially more drastic situation, where infants and potentially small juveniles filled in the niche of small and potentially medium sized aerial predators, but like a sped up, more extreme version of pterosaur evolution, slowly became more adapted to a more grounded life as they matured, bulking up as they grew and having their wing limbs slowly change in function from flying, climbing and walking to mostly climbing, walking and taking down prey, being at best able to let them clumsily glide down from a tall place, depending on their weight and size as fully grown adults.
This way, we solve the problem of bulk, size and flight not working at the same time by simply not tackling them all at the same time. They won't fly forever, and how long they'll fly for will drastically depend on how they're structured, but the fact they're still the same species and the existence of sightings of clearly airborne infants and smaller, lighter juveniles gliding could lead some people to wrongly believe even the large adults could fly, simply choosing not to. I'd still recommend having their wing limbs structured like a pterosaur's and used for walking more than the front limbs at least at first, with the front ones bulking up and playing a more predominant role in walking only in the heavy adults, simply so they could fly for a longer portion of their lives. Still, this is probably the best way available for them to throughly check all of the traits you want for your scientifically plausible dragons, especially since them developing away from flying as they mature would allow them to actually bulk up way more, potentially having more solid, less spongy horns, longer and more flexible tails and becoming even longer than the 20 ft. Length you asked for. Just watch out so they're not too bulky and heavy, unless you don't mind them being slow.
