The federation between mastodon and lemmy is strange. If a M account wants to follow a L community, they need to follow an automated M account which represents the L community. But if any M post mentions that L community, the post will get boosted by the community’s M account, so everybody who follows will get a notification. And I’m not sure if this can be moderated from the L side, because it seems like it never goes through L. Such as - do you see this @opensource ? Does a L mod see this?
You had asked about a ban, which is possible. I’m actually not sure how post removals are interpreted by Mastodon.
That all said, it’s clunky to view one app via the other just because they both “speak” activitypub and recommended to have separate accounts.