You can save posts, at least in the web view of Lemmy but whether a particular app has it or not I don't know. In the web view it's the star icon to the right of the reply button.
I'm using Sync and when it was Sync for reddit I believe it was possible. Perhaps it's now a premium feature, idk. But I'm not paying for premium when the developer goes dark between updates. Not saying his development method is wrong, but it's just not for me.