Fediverse

I'm not an expert on either lemmy or mastodon, but federation and interoperability doesn't mean you can use on account on another client. You need an account on every instance that you want to be active on. However, the federation part of fedi means that you don't have to have an account on instances of the same software (mastodon users can talk to and interact with each other all they want regardless of which instance they're on) and interoperability means that different servers can sometimes do the same thing with some caveats.

Microblogging servers for instance can all pretty much be interoperable if they adhere to a common way of structuring data. For them it doesnt matter if you're on Mastodon or some other server, a post is a post. Peertube or pixelfed which has focuses on other data types (video and images respectively) will be slightly less interoperable, but for instance peertube treats followers from mastodon as subscribers (might have my terminology wrong, they might just call channel subs followers) and videos, comments and likes in peertube would become posts, comments and favorites when interacted with from a mastodon account / server

Lemmy is a bit of a different beast because it's data structures is so different, but presumably up votes would be interpreted as favorites in mastodon, a post is a post with a link at the bottom and threads in mastodon on a lemmy post might even become comment chains when viewed from lemmy, not sure. Someone else can fill in if they know how this works.

Your home instance (feddit.de, if I am not wrong) should add a mastodon instance to federating list before this can happen. This is your current list - https://feddit.de/instances