So, lizardfolk are humanoid (and, so, upright) creatures with reptilian features and are also part-time endotherms. They're well-adapted to living in water and on trees to a degree. One adaptation for of that is a large tail that can be used for swimming. Of course, they can and will use their arms as well.
Now, the problem comes from the fact that lizardfolk are bipedal and I'm afraid their tail could end up throwing them off-balance.
In paper, they can use their tails in a number of different ways, including the aforementioned swimming aid and swiping/flicking it. Since the tail has powerful muscles, these move can be effective at stunning human opponents. I'm not sure if they could create an entire martial art around it though.
The question is, what would a lizardfolk's tail actually look like then and how would it avoid causing problems with the creature's balance?
Note: Despite what some people think, lizardfolk do have emotions, though they have trouble communicating them. For that very reason, they tend to avoid social media in every shape or form.
Note: How these lizardfolk are supposed too look like?
In terms of posture, I had the argoninans from Skyrim in mind. However, the reptilian features, like scale type, patterns, color, head shape and tail type came from the Asian water monitor.