Well, yeah, you could rewrite every link that's displayed. So, if someone links to https://the-link-you-want-to-go-to.com/, then your instance would basically make that link instead point to https://your-instance.com/outgoing?url=https://the-link-you-want-to-go-to.com/.

And then your instance's server would do the check and redirect you accordingly.

But the downsides are then:

• It's slow. Instead of links opening directly, all of them need to redirect first.
• It increases the server load.
• It allows instances to track which links you click on. (And this is what such link rewriting is often used for. People here would absolutely riot.)

And well, in theory there's nothing stopping Lemmy from displaying posts from Mastodon or other Fediverse services. You can just request their data from the federated server via ActivityPub.

In practice, though, it's not always easy to display these posts in the UI of a different service. For example, Mastodon posts only show up on Lemmy, if the person who created the post tagged a specific Lemmy community, because you kind of want them to show up as part of a specific community.
On the other hand, Kbin is a piece of software that federates well with Lemmy, because they offer a similar user experience, and of course a lot of development time got invested into ensuring compatibility.
Federation with other Fediverse services are not supported yet, to my knowledge.