Controller input lag on Lg 120hz 65" (Xbox one)

You might try enabling the screen's "game mode" if one is available...

https/displaylag.com/how-to-enable-game-mode-on-your-hdtv/

If there isn't a specific gaming mode, you might try disabling various post-processing image enhancements, and see if that improves the input lag.

1) As said, attempt to find game mode, though there MIGHT be some settings that help.

2) *If you have "Motion Smoothing" enabled disable this. It adds a LOT of lag as it must buffer several frames to analyze then create an extra frame that fits in between two real ones.

(BTW, even if you had a gaming PC it would still show 60FPS if locked with VSYNC since all this processing is internal to the HDTV. So it's a 60Hz/60FPS signal that turns into a 120Hz/120FPS on the actual HDTV)

This feature should only be used for SPORTS as it makes movies and even TV shows look incorrect. Movies especially since the motion blur is calibrated to the FPS (the lower the FPS the higher the blur as our brains internally get saturated with data. If the data is low enough such as lower FPS we add blur so it "works out" in our heads to look as realistic as possible).

3) If neither solution seems to work then the 4K video processor in the HDTV may be just too slow.

4) I believe the XBOX ONE S has an option to scale to 4K internally (UHD mode?) which sends a 4K signal rather than a 1080p HDTV signal that the HDTV upscales.

That may or may not help for latency though there MAY be a visual difference.