I don't know of a single switch for what you want to do. You should be able accomplish what you want by turning off "Use Cellular Data", pausing the sync while avoiding turning it back on and ensuring your phone does not connect to WiFi for data. You might also try signing out of your account on your phone.
It is hard to say what will happen long term when you disable so much of the app.
Why do you want to do that? Lightroom mobile depends on the cloud for things like searching by keyword, and if you do not sync, then your images are not stored safely in the cloud, but only on your device. That could make you lose all your images. And if you use iCloud backup for added safety, then they are in the cloud anyway, just on a different server.