So this got born out of the question of direct messages. Intuitively, I would expect those to just work, a user is a user, a message is a message. As far as I can tell, you can't direct message. I haven't played around with mentions yet. As far as viewing posts, its bad both ways. For example, this is the only post I see in this community from Mastodon. I think that is due to the same discovery issues throughout the fediverse, that is, if you don't already know about it, you won't find it. And when you discover, you might only see new things unless interactions are done to old things.
For lemmy, the UI and the server are completely separate. There is a moderately well documented API for interacting directly with the server.
Some kind of unified account creation would help with this, I think. Something where you create an account somewhere "central" (which I get is kind of antithetical to the fediverse mentality, but work with me here), and then can "link" that account to multiple fediverse servers.
Right now, I can create an account on pawb, and I can create an account on yiffit, but even though they might have the same username, they're completely separate. It'd be ideal to be able to link those both to a single 'meta' account, which would then allow me to log into and browse either service, while maintaining a unified post history, etc.
Basically, someone clicking my profile on either service would see my global post history across all fediverse services I'd linked.
This could indirectly assist with the discoverability issue slightly. Rather than being on Mastodon, trying to view Lemmy threads, and seeing only new things where specific tags were used, the user could link their account to Lemmy servers (or other Mastodon servers or whatever), and be able to use one unified identity to browse each of those services independently.
Technically there's nothing stopping someone from having accounts on multiple services now, but having those accounts be completely independent kind of defeats the purpose.
I haven’t yet found a way to view Mastodon posts on Lemmy
Lemmy doesn't have any kind of interoperability with Mastodon (outside of the specific use case you mention), but kbin has interoperability with both Lemmy and Mastodon content, for what it's worth.