No, there is no centralised account service for the Fediverse, the accounts are owned by the individual websites (so in your case, lemmy.ml). The different softwares can then interact over the ActivityPub protocol, but how this works depends on the two softwares and what is currently implemented.

Lemmy currently cannot interact with Mastodon directly, but Lemmy communities and users will show up on Mastodon for people to follow and interact with. Lemmy users can interact with posts and comments that Mastodon users post on Lemmy though.

but creating a lemmy post isn’t possible

That’s not true, it definitely is possible. There have been multiple test posts I’ve seen pop up, even in this specific community, of people posting to here from Mastodon (or similar) fedi accounts.

The format appears to be this:

Title Goes Here

https://link-goes-here.example/ (optional)

Content goes here

@community@lemmy-instance-here.example

At the end you just need to mention the community (or communities?) you want to post to, and the community will boost your post, making it show up in its timeline / feed.

but to follow you need a mastodon account

I think this is because Lemmy has been designed community-first but there’s certainly the possibility of allowing following non-communities in the future.

For now, creating another account isn’t that much overhead so I’d say just bite the bullet if you want both the Lemmy experience and Mastodon experience. Interestingly enough, some fedi software supports different frontends (websites that you actually interact with) and I wonder if this would be possible with Lemmy as well. For example, I’m on a Pleroma server and it offers both a Pleroma frontend and a Mastodon one, if you prefer that. We’ll have to see what the future brings.