The will.
Or at least they can, and do, sometimes, if you have good MOV karma..
Why not supply a little more info, like:
* Which OS
* Which version of Lightroom
* History of MOV files.
* Export format.
* Do other video types export OK
* How many different MOV files have you tried - all with the same history?
and of course:
* What, exactly, happens, when you try?
Rob.