I have seen some discussions about Middle Earth's Erebor, the "lonely mountain" and how it really isn't lonely. How could a true "Lonely Mountain" (a single peak in the middle of a vast plain) form? My theory involves a shield volcano and huge amounts of erosion, but that would take billions of years.
Kilimanjaro is a "fairly lonely mountain". From a distance, it looks like it just stands in the middle of the African plain. Get closer, and you can see the smaller mountains of the Virunga region nearby, but from a hundred kilometers, it's hard to see the mountain as anything but "lonely".
Kilimanjaro isn't a shield volcano, it's a stratovolcano. Stratovolcano formation (like the Cascades and Andes volcanoes, Popocatepetl, and Fujiyama) depends on subduction, but it can produce mountains like Rainier and Hood, tall, rising from low lands near sea level, and not close to a recognized mountain range (the Cascades proper are 60-70 km east of Rainier, for instance).
Similarly, Mount Fuji is hard to see as anything but a "lonely mountain" -- and its conical, snow-topped peak (well, until the 1980s or so) is so iconic that it's been a national symbol for centuries.
Such mountains occur above the line where a subducting section of oceanic crust begins to melt as it plunges into the mantle. Because of the linear nature of subduction zones, they tend to occur in rows, but they're often a hundred or more kilometers apart -- far enough that you'll generally only see one or two in the distance from anywhere along the range.
In the Andes, the volcanoes coincide more closely with the fold mountains of the general range, but in North America, they generally stand out. You'll never see a mountain so alone you can't see another from its upper slopes -- but you can have them far enough apart that each one seems "lonely".
Have a geological hot spot sitting under a relatively stationary tectonic plate.
Those hot spots are areas beneath the Earth's crust where the magma is particularly hot. This causes the magma at that location to push up through the crust and create a volcano. This is seen a lot in the Pacific island chains, Hawaii being a very visible (and still active) example.
The reason this typically creates chains of volcanos rather than individual ones is that the tectonic plates are moving relative to that hot spot. This causes a volcanic chain rather than a single island or mountain (note that islands are just underwater mountains tall enough to reach the surface). If that tectonic plate and the hot spot were stationary relative to one another, then you'd just see a very large volcano instead.
The downside of this is that the inside of the mountain would likely be a very dangerous place to live, since it's still an active volcano. I don't think even Tolkien's dwarves would be that foolhardy. That said, it's possible that the hot spot did eventually cool enough to make the volcano dormant or even inactive, in which case you very well could have a true Lonely Mountain.
Having said that, do note that I am not an expert.
Stratovolcano seems to be a better fit for the "Lone Mountain" or Tolkien lore than the shield volcano. Shield volcanoes are very gradual, I don't think they match the idea of a mountain depicted in Tolkien's work.
There are real life examples of standalone stratovolcanoes, like Mount Kilimanjaro.
As an alternative to the stratovolcano, lone peaks can form from an intrusion of hard rock into soft rock (e.g. igneous into sedimentary). If the soft rock layer then becomes exposed, and erodes away, the intrusion is left standing. A famous example is Devil's tower (from Close Encounters):
This doesn't look very Middle Earthy (and is probably too small to house Erebor). But other mountains (like the Mont Blanc) are also formed (partly) from intrusions. If conditions are just right, you might get an isolated granite intrusion the size of the Lonely Mountain.
Not really sure if it fits, but Sandia mountain just to the east of Albuquerque might give you something.
Sandia and Manzano are two connected mountains that are several miles from other nearby mountains. As I understand it, they formed by two plates hitting each other and pushing up, like a lot of other ranges. Sandia is unusual in that the western plate seems to have slipped back down, creating the plain that the City of Albuquerque sits on.
Here is how I see it fitting in your world. A part of plate A, a corner of the plate is made of relatively hard or rigid rock. It is moving east. Another corner of a different plate is shifting west. The corners hit, pushing each other upward and create a triangular tent like shape over the course of, well, however long it takes for mountains to be created by plate impact. Geology is just physics slowed down with a few trees on top.
The key is that it is the impact of 2 corners hitting, rather than an edge to edge action that creates whole ranges. the two corners, I would imagine, pushing up against each other should form a roughly triangular cone.
The area could still be active in a slow sense. Geological time could allow for Dwarves to arrive, carve out a huge hall, be driven out by a huge dragon, and return to be driven mad by the Arkenstone, all without the more exciting physics involved with a volcanic cone.
This is just imagination, of course. I'm no geologist and will be happy to be corrected. But this is how I could see a Lonely Mountain coming to be, without the need for volcanic activity. the Volcanic stuff, of course, belongs in Mordor.
Erebor is NOT "a single peak in the middle of a vast plain". If you look at Tolkien's maps, you see that not far to the north and west, there's a mountain range, an offshoot of the Misty Mountains. To the east are the Iron Hills, while there appears to be hilly country to the southeast.
As the other answers have said, a stratovolcano seems to be the best fit, especially since (if I remember correctly) Bilbo's account mentions smokes and fumes coming from the mountain, seemingly in too great a quantity to be produced by one sleepy dragon.
I'd suggest Mount Shasta https://en.wikipedia.org/wiki/Mount_Shasta might be a better (or at least more familiar) parallel to Erebor than Kilimanjaro, since it has large plains to the north and (some distance to) south, is close to the Coast Ranges to the west, and is at the northern extremity of the Sierra Nevada (or perhaps the southern extremity of the Cascades).