I haven't noticed a problem with audio sync, but that might be because of what audio option I am using, or the local feed is good, or I have watched so many dubbed Japanese Godzilla / Mothra / Mechagodzilla / Starman movies that I seldom pay attention to lip movements vs. sound unless it is radically off. But then I am in Salem, Oregon and receive TCM HD on 784 so I am on a different headend than you are on.
This appears to be the place where you can let TCM know you have issues with viewing their channel on your TV, with lots of space where you can describe your access to TCM (cable company, cable company's equipment and your equipment), your location, and a description of the problem:
Edited to add: Yes, the lips move about 3/10ths of a second before the sound, even here in Salem, Oregon, Comcast HD channel 784. This is observed in movie "Kim".
Edited to add: Also with the intro and playing of "The Day The Earth Stood Still" (1951), sound is 1/3rd second late (and quite obvious when the phone hook is hit several times in the beginning of the movie). I'm putting in a ticket at the above URL.
Edited to add: But TCM (SD) 501 has the sound synced perfectly to the lips, so it is just 784 (HD) that is off with video about 1/3rd of a second sooner than the sound.