Lemmy doesn’t do microblogging.

You cannot follow the entire instance as such, rather the individual accounts on the instance - such as @BBCRD, @BBC_News_Labs, @Connected_Studio etc.

Kbin users can subscribe to whatever content is shared from social.bbc on federated instances by subscribing to /d/social.bbc, but I’m not sure how much sense that makes. :)

Edit: In Lemmy you’d find the users by entering for example /u/BBCRD@social.bbc, but as @roguetrick pointed out Lemmy is not really made for microblogging.

Unsure if you can follow entire instances but you can definitely follow users from that instance such as https://kbin.social/u/@BBCRD@social.bbc

No expert, but I have a Mastodon account + app and a Lemmy account + app.