Is the 360 connected directly to the TV or through a soundbar or any other A/V equipment.
If it's connected directly to the TV use a non ARC HDMI connector and set the 360 Dolby setting to follow content, you can try all 3 if this doesn't work.
If you are using a soundbar if you have a HDMI IN connector then connect the 360 to that and then soundbar to the TV.
I have a LG TV and soundbar with the 360 connected to the TV and the TV and soundbar connected using the HDMI eARC connector with no problems but some people do have sync problems using HDMI ARC.
If you still have problems you can try using a fibre optical cable directly from the 360 to the soundbar, the optical connector on the TV is probably just an output. The other solution some people have to use is turn Dolby to off, not something you want to do if you have paid for a soundbar.