Yes, Piefed does. So does NodeBB. And Catodon.

So, from a Mastodon-based website, you can just follow a group hosted on a Lemmy- (or Piefed-, or NodeBB-, or Catodon-) based website just by searching for the group's address, i.e, @fediverse@lemmy.wrold. Mastodon does not have robust support for groups, so they just look like users or bots there. Interacting with a group works the same way as interacting with a user account. You can reply to posts the way you'd reply to a regular Mastodon post, because, from Mastodon's point of view, it is a regular Mastodon post.

More broadly, this space all makes a lot more sense when you stop thinking of it as a handful of platforms and start thinking of it as thousands and thousands of individual websites that mirror content. Content itself is, generally, independent of platform, and content is really only accessible if it is being mirrored on your home server -- you are very rarely accessing interacting with remotely hosted content, you are interacting with local copies of remote content. This means accessing remote originating content can involve a bit more deliberate thought than one might expect from a centralized, single-website platform (like, say, Twitter).

Now, there are many reasons someone might want to set up and operate a website that can communicate with the Fediverse, and not all of them involve wanting to be part of the big network here. Like, maybe they want to set up their own network! And there is a lot of content out there on other websites that no one on your website gives a damn about, so why would you bother wasting your bandwidth collecting it or drive space storing it? This means content does not automatically get sent everywhere.

To get content from remote websites, you have to subscribe to the content generator or, in the case of groups like this here on Lemmy, the content container. So, to find that content, you have to go searching other websites to see what they have, and then come back to your host and subscribe by searching for the address of what you want to have sent to you.

e.g. searching for @fediverse@lemmmy.world in your host's search bar should bring this group up, and then you can subscribe to it by clicking on 'follow'.

I would encourage people, though, to try out different websites or server softwares to see what works best for them. Mastodon, Lemmy, Piefed, Catodon, Misskey, Hometown, Friendica, Mbin, or others.

Also, I encourage people to check out sites that focus on aping other types of websites: NodeBB for forums; Pixelfed, for image sharing (i.e. federated Instagram); Harmony for chat (Discord); PeerTube for video (YouTube); Loops for video shorts (Tiktok); Owncast for streaming (Twitch); Bookwyrm for book reviews (Goodreads); Bowrd for interest boards (Pinterest); Inkwell for blogging (Blogger), or Wordpress plus the Fediverse plugin; Ghost for newsletters (substack); Mobilizon for events (Eventbrite); Funkwhale for music and podcasts (Soundcloud); Cookified for recipes. There's a whole ecosystem here of small websites, built for sharing, and software that lets people stand up sharing sites of their own.