Apple TV APP

You do not need the Apple TV hardware, if the Apple TV app came reinstalled on your TV set, or streaming device. You do need to have an internet service connected and you will need to set up an Apple ID account. See the instructions below.

Set up the Apple TV app on your smart TV or streaming device:

https://support.apple.com/en-us/HT209440

You do need the Apple TV set-top box (4th generation or later) to install the tvOS Spectrum TV app.

The Apple TV app on your LG only gives access to iTunes Store movies and TV shows for buy and rent, Apple TV+, and additional premium Apple TV app Channels that you may wish to subscribe to. The Apple TV app on your LG does not give you access to the Spectrum channels that you pay Spectrum for.

the apple tv app is an app that runs on other smart tv

the appletv box is a box that support apps like I suppose your spectrum app

the appletv app does not support apps, if your spectrum app is not available on your LG TV smart tv

then you need to purchase a setup box which has the app available.