Just like the guy with the third party controller, I've got a dead zone when moving my joystick to the upper left. I'll be just zippin right on through spear traps, flame pits, and spike panels but I'll approach a chasm and attempt to leap over only to stop dead in midair and plummet to my death. Actually, I'm not sure if that's what a dead zone is, this particular spot makes lara stop in her tracks, no matter what I'm doing. If I move my joystick to the most natural position to make her move to the upper left, she stops. I have to wrestle with it to get her to move to the upper left and its a battle every time any sort of change in momentum is required.
This doesn't happen on other games, I tested another DS controller, same issue, and here's some weirdness that I need to verify but I'm almost positive I'm remembering it correctly; in Tomb Raider 2013 Multiplayer (I cant remember if it affects single player), I have the same issue. I'll check to make sure its the same direction but its just some extra info to give you in case it helps to identify the cause.