Artemis is supposed to support kbin and Lemmy. If it doesn't support Lemmy right away, then it wouldn't help to register on a Lemmy instance, because Artemis still wouldn't support Lemmy.
You're right that you can't sign into a Lemmy instance with your kbin credentials. Each site is it's own site. If something is posted on lemmy.world, it sends a notice to kbin.social and kbin.social fetches the info and publishes it locally on kbin as well. Comments on the kbin post are sent back to lemmy.world. There's basically a copy of the post and comments on every server. Not every server will "know" about every other server though, so content could push across the entire federated network slowly sometimes.
PleaseSandwich