Being a Comcast HD cable box user, the Motorola DCT-34XX(DVR) boxes to NOT have a lip sync function. Several channels on HD that I get have issues, though you can't tell if it is from the source, or caused by Comcast. I feed all my audio/video through a Denon 3803(soon to be replaced by a 990/7075), so I can adjust lip sync per input when needed.

I don't know of any cable boxes with a lip sync adjustment - none of mine have, and I've used my 990's lip sync adjustment to address lip sync delays from both my old Pace DC550 and my current SA 8300HD. We also had one local station that often had broadcast problems that included a significant lip sync issue with HD content, but they have fortunately fixed that...