It seems like I should be able to subscribe to a Mastodon channel on Lemmy, but according to this answer from 2 months ago, that isn't part of Lemmy's general direction:
In the meantime, if you want both reddit like and twitter like functionality, checkout kbin. Kbin federates with both lemmy and mastodon and has both magazines (their version of communities) and microblogging (like twitter/mastodon)