Unfortunately what you would like to do is not possible as LG TVs have WebOS. Even if we would make Hue Essentials compatible with this, we would need to look into it if they have any developer APIs for screen recording in order to get the Sync working. I am not aware of such APIs on LG TVs.
What you can do instead is use an external Android TV like the NVIDIA SHIELD Android TV (Pro). See: Sync (Entertainment) on your phone or Android TV