If a hero or monster is aware of a pit, it may jump across the pit for three movement points for each space crossed. Simply place the figure on the other side of the pit after spending the movement points?

Strict reading of the JitD rules.... only pits can be jumped. Water can't be.

Have there been any other rulings on this for expansion obstacles I've not come across? Mud is effectively jumping anyway. Lava? Not having played WoD6, I've never really thought about it. Ice?

Water specifically cannot be jumped; as per the FAQ:

Q: Why can’t I jump over water like I can pits?
A: As every hero knows, the dank water found in subterranean caverns is usually infested with deadly bloodsquids, ready to pull an unwary hero to his doom at a moment’s notice. As a result, only the most acrobatic heroes dare to leap across even the most innocent-seeming pools of water.

Lava, mud, and ice can all be jumped, as per their respective rulebooks. Scything blades and dart fields cannot.