I wouldn't lock either axis if it can be avoided, but braking and throttle are definitely a lot easier to modulate by the rider than keeping the bike perfectly angled. The biggest thing I think will be the shorter, stiffer suspension on the bike, ie potholes, speedbumps, dips, etc. I havent thought of a good way to allow movement in 3 axis, apart from just suspending the thing on springs. For now I'll just worry about roll.
I'm much more of a motorcyclist than I am a physicist. This project to me seems like a great way for me to learn. If someone can help me figure out all the parts I need so we can get this whole thing built, we can test out everything in reality instead of just talking about it on the forums. I'm excited to work with arduinos and everything else.