With any simulation, there will generally be a point where the model you are using breaks down. I think that happens with LFS with lower tire pressures.
There are many systems in the world that depending on external conditions will change their behavior dramatically. A simple example is water. It is a liquid. Make it cold enough, it changes from a liquid to a solid. If you water simulator does not take that change into account, you will get some odd results.
I think that LFS models tires pretty darned well, but in certain cases, the model breaks down. I doubt there is much in the system about deformation due to low pressures, material flex, bead adhesion, etc. Plus, tires change how they react dramatically with pressure. It would be hard to completely model all of that realistically.
My suggestion for LFS is to limit the usable tire pressure range for each tire type. Then work on the heating algorithms a bit to tweak them in a bit better. That way, you wouldn't be able to use an unrealistic tire pressure to gain advantage and it would be the same for everybody. (Nobody IRL drives a street car on the track with only 22psi in the tires)
You also wouldn't have to try to model super low tire pressures in the system completely because you either have a reasonable tire pressure, or the tire is flat.
Maybe just tweaking the temperature and sidewall behavior would be enough, but limiting the tire pressure range would be effective too.