App store missing in Apple TV on new LG tv

The Apple TV app on smart TVs is not a full replacement of the Apple TV set-top box. You will need that latter to use Apple App Store apps. If the LG Content Store doesn’t offer that app, then you will need to attach an HMDI device that does offer that app, such as the Apple TV box.

Your TV has access to the Apple TV app, which lets you access your previous iTunes TV show and movie purchases as well as rentals. It also lets you subscribe to Apple TV Channels. You don't get access to their app store, which is only available on the Apple TV Hardware, which has content specifically developed for that platform. You would only have access to the app store that is on your LG TV, which is where you downloaded the Apple TV app. You would need to search there for further apps.