While Mastodon, Lemmy, Misskey and a lot other software plattforms are connected in the Fediverse. You should be aware, that different software work different on the Fediverse. Mastodon is designed liker Twitter/X, to be a Plattform posint short messages or news. Lemmy is more designed like a forum, not as user based as Mastodon, more in communities. There is a connection between a lot different Software Platforms on the Fediverse, but not every feature is on every plattform. So you are not able to downvote a Lemmy post from Mastodon. You have the option to interact with Lemmy posts with a Mastodon account and it’s a valid way to do it, but for the full experience on all Plattform, you should make yourself an account on every Plattform that is important for you.
I have never used the Mastodon app, i think a lot 3rd Party apps are better on Mastodon, so i don’t know how it looks, but Mastodon has, or had, a weird form in showing commet trees in my opinion.