No, there's no way to avoid it. It's a game engine bug, which means it can only be fixed by Bethesda (even for PC users). Unfortunately, any chance of that happening vanished over a year ago now.
http://www.gamesas.com/topic/1502140-regarding-the-lip-sync-bug-6/
Not only that but it also seems not to affect every game either. Some folks seem to get hit by the bug all the time, other folks not very often. I have played a few games (PC) where I could not notice it at all. But in other games it was very noticeable.
There is a series of threads dedicated to the topic: http://www.gamesas.com/topic/1502140-regarding-the-lip-sync-bug-6/
Seems like the problem can't be resolved