Changing a truck cab

Would it be better to take the doors off? Or to leave them on? I guess if I leave them on, I'd want to have them open, since lifting the cab with the straps run through the door window openings might pull the door up and mess up the hinges/door alignment?

You're right,you don't want to run the straps through the window openings in the door.You could leave the doors on and have them open and you should be fine but,like the previous poster said,if you need to do any work on them that would be good time to pull them off.
The two doors might weigh 150 lbs combined so it won't make or break anything that the cab itself would'nt.