As far as I know Lemmy stores only text locally and images and such will be linked to the external instance. Text doesn’t use much disk space, so that shouldn’t be a big a problem. Sometimes when you browse Lemmy, you notice posts that have broken links to images. It’s because the other instance is down, but you can still see the text portion of the posts on your home instance.

There’s also pornlemmy.com. You don’t need to be logged in to view posts and there’s no anime/hentai or aigen stuff.

It’s not a feature of Lemmy and, I guess, no-one has wanted to create it for their app. You should submit this idea to the Lemmy developers so it will eventually be a feature in every app.