The "steering while stopped" behavior is due to torsional stiffness. Here's data from a couple of tires measured where the tire is stationary with some load applied, then twisted through different angles:
http://www.performancesimulations.com/files/tiretorsion1.JPG
This sort of works a bit hand in hand with aligning torque in reality, but is not typically very important or noticeable at anything approaching racing speeds since it really has more to do with how quickly you steer the wheel than what the slip angle is. If you were doing a driving simulator for very low speed driving it'd be a nice touch to include, but the aligning torque when the wheel is rolling is much more important.
In LFS and most other sims I just use spring centering FFB, so don't have any LFS specific comments on this.
http://www.performancesimulations.com/files/tiretorsion1.JPG
This sort of works a bit hand in hand with aligning torque in reality, but is not typically very important or noticeable at anything approaching racing speeds since it really has more to do with how quickly you steer the wheel than what the slip angle is. If you were doing a driving simulator for very low speed driving it'd be a nice touch to include, but the aligning torque when the wheel is rolling is much more important.
In LFS and most other sims I just use spring centering FFB, so don't have any LFS specific comments on this.