I suddenly was having major issues with lip sync, sound ahead of picture. I could not figure out what had changed. My settings on my audio system were the same, I did not change anything on my TV. Netflix, HBO Max, etc were all in sync so I restarted the DVR server thinking it was a problem there. No change. Then after 2 days of dealing with this issue I found the problem. At some point the audio driver on Channels got changed to default instead of on experimental. I put it back to experimental and lip sync is perfect again. I never saw this issue before when switching drivers, but it works correctly now.
I'm having the sync problems as well, but mine is lagging and it isn't static, it is cumulative, and it doesn't always happen, but happens more often than not. Setup is LG E7 OLED 4K TV, Apple TV 4K (2021 edition) connected to HDMI 1, HDHomeRun FLEX 4K (OTA), HDHomeRun Prime (Cable). Everything updated to the latest firmware. The symptoms are when everything is powered on, everything is fine and works as expected, but after 10 to 15 minutes you can start to tell that the audio is starting to lag behind the video. If you let it go, the lag gets worse. After an hour, the audio is a good minute behind the video.
If you change channels or exit the app and reenter, everything syncs back up and then starts lag over time again. The lagging happens on both OTA and Cable, though a couple times I've had it where the lagging would happen on OTA, but not Cable as well as had it happen the other way around.
I'm not having problems with this lagging in other apps currently, though I had the exact same issue with the NFL app starting around mid to late October last year with my other older Apple TV 4K, which I reported weekly for the rest of the season, but they never fixed before the end of the season.
This is a really frustrating problem because I have tried multiple settings changes to try to fix it, yet nothing has worked so far, and as I have said, it doesn't happen with any other streaming app, other than NFL.
Are you using the TV speakers for sound or do you have a sound system or sound bar of some kind?
It happens both with using the TV speakers and through a Yamaha A1070 amp. Right now it is set up with the Apple TV connected to HDMI 1 on the TV and the TV connected to the amp from HDMI 2 for ARC connection. I've had to change to this setup because LG pushed a firmware that breaks Dolby Vision with Apple TVs if they are running through an amp. It also happened when the Apple TV was connected to the amp prior to the LG firmware update.