Check your Settings on the LG to for Dolby Vision settings. The UI and Preview of the app uses a normal video signal, while most movies are encoded with Dolby Vision. You most likely have Film Maker mode auto start turned on. The setting is somewhere in Picture > Advanced Settings > Film Maker Mode Auto Start. When this setting is turned on, it will automatically change to Film Maker mode and appear darker on the screen. Shut that off and change your picture mode to something like Standard or Vivid for a brighter picture.
There is not settings on the Apple TV app for the picture, so you will need to experiment with the TV.