Lemmy and Mastodon servers are capable of speaking to each other using the ActivityPub protocol, but they present substantially different APIs and user interfaces to the end user. There is no way to use a Lemmy app to log in to a Mastodon instance, or vice versa.
Mastodon has no concept of communities whatsoever, nor any features which derive from them (like community level moderators, or directing your comments towards various communities instead of your timeline). It doesn't distinguish between "posts" and "comments." Its moderation / reporting system works very differently. Media uploading, alternate text, etc work very differently. and so on and so on.
Comments / replies can be seen/shared from one platform to another, but the various ways users interact with them are quite different.