How do I know if my lg tv is compatible

1. If you mean AirPlay compatible, then have the exact TV model number ready, and see the list at: List of AirPlay 2-enabled smart TVs - Apple
2. If you mean supporting the Apple TV app natively among its smart apps, then see the list at: List of Apple TV app-supported devices - Apple
3. If you mean compatible with the Apple TV box, then any HDTV with HDMI is compatible. Set up your Apple TV - Apple Support
4. If you mean the software remote on your iPhone, then that is for the Apple TV box (3rd generation or later). Set up the Apple TV Remote on your iPhone, iPad, or iPod touch - Apple Support
5. There may be different remote apps for iPhone that are tailored for LG TVs. LG remote apps - LG Support. And alternatively from third party developers as well. Get apps in the App Store on iPhone - Apple Support

if it's on the list

Apple TV app - Devices - Apple