My tv says Apple TV app not compatible with my LG 55UK6500UAU. What do I use to connect?

List of Apple TV app-supported devices - Apple

I’m no expert of LG model numbering, but from what I understand of it, LG55UK6500 seems to be in the “UK62 and above” category, thereby listed as ‘supported’.

See your manual on how to update firmware and separately update apps as well, if applicable.