Lemmy stores your posts and replies on both your host server and on the server of the community.
One interesting behavior to note here that is different from reddit is that while comments on reddit belong to the profile of the person commenting and is then imported to view in the subreddit (this is why you can edit comments after being banned, and why there visible in your profile even if removed from a subreddit), on lemmy the target community is instead authoritative and your host server will by default respect a deletion by community mods on different servers by also removing that comment from your profile.