LP and MK are unresponsive during gameplay? Alrighty.
How do I fix it?
Set "Right Stick Assists" to Off, in button config.
-or-
Try adding "-vjoyfix" (without the quotes) as a Launch Option in Steam.
-or-
Map "Right stick up" and "Right stick down" to some real input, rather than leaving them unmapped.
OK, so what's the problem?
Your controller driver is reporting bogus information for POV hats, when there is really no information to report for them. VJoy does this by default. As a result, the game thinks your right stick is always pressed upward, and if you have Right Stick Assists on that counts as pressing Assist 1, which is LP+MK. Turning off Right Stick Assists or doing the other things mentioned as solutions ignores this bogus info.
Thanks ninjamunky for bringing the problem to my attention, and Muro for the solution!