Apps? As on your phone? No, that's not the way it works. You can host your own instance. I would in fact recommend it, if possible. It would give you the best Lemmy experience possible. But here's the thing: the machine where you run the instance has to be on 24/7 or as closely to that as possible, it isn't enough for it to be online when you'd browse Lemmy.

Here's an oversimplified explanation of how federation works: say your personal instance is disappointingintro.com and you're federated with lemmy.world. Any time something happens on the lemmy.world server (upvotes, comments, posts...), the lemmy.world server will send a "message" to the disappointingintro one notifying it of what just happened. The disappointingintro server has a copy of everyting coming from lemmy.world, where all of these updates are written into. When you view a lemmy.world community on disappointingintro what you're really viewing is this copy.

Because of this, if your instance was hosted on a phone, said phone would need to communicate constantly with the federation. If it didn't you'd miss out on a ton of updates and you'd only see a fraction of the content.

The actual way to do this is either to self host it (meaning installing the server on an older PC or laptop lying somewhere in your basement), assuming you know how to do that, or rent a server from someone else to host it on their server for you. Both take some degrees of technical expertise and have some expenses, which is why public instances exist, most users can't be bothered running their own instance.