How can I watch the Lifetime Movie Channel on Apple TV?

Yeah; this stuff is confusing, and getting more confusing, eh?

There are some different ways to do this, and which way works best for you can vary.

Here is how to use the Apple TV app, and also how to subscribe to content using the Apple TV app:

Apple TV app for smart TVs and other devices - Apple Support

But… You might already have this LMN streaming service as part of some other subscription or some other package you already have, as services including Hulu, AT&T TV, and some other streaming and content providers can or do include LMN in their packages; there can be different ways to access the content. AT&T can include content streaming with some of their cellphone plans, for instance.

Here is a write-up on some if the ways to get at LMN:

https://thestreamable.com/channels/lifetime-movie-network

And here is how to access the LG content app store for purchases and subscriptions:

https://www.lg.com/us/support/video-tutorials/lg-tv-content-store-webos-2-0-CT10000020-1433189305595

https://www.lg.com/us/support/help-library/using-lg-content-store-with-webos-60-CT10000020-20152366129037

The Apple TV app features an in-app channel “Lifetime Movie Club”, which is different from the Lifetime Movie Network channel. One requires a subscription started in the Apple TV app, while the other requires a subscription with a pay TV provider (cable or otherwise) and is not available directly in the Apple TV app. One has on-demand content, while the other has a linear TV schedule.

Do you have the Apple TV box? If so, which model? Identify your Apple TV model - Apple Support.

Or do you have (use) the Apple TV app on your smart TV? Subscribe to Apple TV channels in the Apple TV app - Apple Support.

These have different capabilities. Apple TV app vs. Apple TV box - Apple Community.