HTIB boxes usually are intentionally simplified in order to keep the cost down. I did manage to download the HTIB's manual and couldn't find any mention of an auto lip sync feature, only fixed sync delays. You might want to consider getting an audio/video receiver which includes that feature. It'll probably be significantly more expensive, though, because of the other features it includes, too. Sorry, I don't know enough about the features in the less expensive AVR models to be able to make a recommendation.
Marantz SR7009/7.1.4/FH+TM/DefTech PM1000/LCR+TM amped