Lip Sync problems are incrediblely frustrating. I'd assumed it was one of the earlier AppleTVs as they ditched optical out after AppleTV 3.
Oddly I've recently used Airplay to send audio to my Nova with AppleTV 4 4k and the sync seems excellent, not sure if the Airplay 2 capability has somehow improved things on the AppleTV end but in the past lip sync was very bad when I tried to Airplay audio to the Nova.
With AV material going through an AV amp/processor as standard the problem used to be one of the audio being processed quickly onboard the amp/processor but image processing on the attached display (no audio or audio muted) taking several tens of ms longer thus the sound would be ahead of the lips - depending on video processing modes this could be better or worse, the more processing generally taking longer and making lip sync worse. Of numerous DVD/BluRay/media players I've had, and AV amps I've used, as far as I can recall the majority only had the ability to delay audio playback which would compensate for slower image processing on the display device.
Your issue clearly needs a source/intermediate box which can be adjusted to send the audio ahead of time - potentially however the setting on your TV allowing +/- 100 delay may help . What surprises me is how slow the optical audio out/processing must be compared to the TV's video processing which would generally be slower. I don't recall the menus exactly but could the delay be caused by downmixing a 5.1 or higher audio track to stereo on the source devices to output over optical? If the boxes have such settings it may be worth ensuring you are playing stereo audio tracks not multi-channel down mixed - I don't think the Nova etc handle multi-channel audio themselves, though if they do ensuring they are not having to down mix themselves might help. Naturally on the sources you'd want all lip sync settings to be at 0 ms if you can only slow audio as any higher would make it worse.