I'll try and give as good a rundown as I can (and I have no idea how technically inclined you are—if I come across as patronizing, I apologize in advance!) I'm also assuming that you have experience with Reddit.

You are signed up on the lemm.ee instance, which means that you must post/comment from that root domain, or that lemm.ee should be the leftmost text in your url.

Lemmy operates on a similar idea to email, where it doesn't matter where you sign up to start emailing, only that you stay on the same website to email even if you want to communicate with people on other companies' emails.

This is comparable to staying on mail.google.com to send emails to someone on yahoo or hotmail or whatever. We'll stay with this analogy for now: lemm.ee = gmail, and other instances (lemmy.world, lemmy.blahaj.zone, etc.) = yahoo.

— Everyone with an email address will be able to communicate to other email address holders in an email-like fashion. — Similarly, everyone with a Lemmy account will be able to communicate with other Lemmy users in a Lemmy-like fashion, so long as both Lemmy instances are federated with each other.

What is confusing currently is that every version of Lemmy looks largely the same, but the storage in those other Lemmy instances does not store your account information.

And, to complicate this further: Lemmy does not convert links to other Lemmy posts in other instances so that it leads to your instance's version: as a loose analogy, it would be like if trying to reply to an email, sent from a yahoo account, would send you to Yahoo Mail (the website), even if you were signed into Gmail. This is why it looks like you're signed out of Lemmy even if everything looks similar—you were taken out of Gmail and dumped into Yahoo Mail. You need to go back to Gmail's version of the email thread and reply from there.

Having this idea working is still a work in progress, and I'm not 100% sure how they'll be able to sort that out. What you can try and do in the meantime is to copy the URL of the thread that you're trying to reply to, and search for that URL in your instance.

To zoom out a bit more, social networks like Mastodon and Kbin use a similar protocol, but not quite—and this is where the email analogy kind of falls apart. As Kbin and Lemmy operate very similarly, the developers of both have done a little work to allow for users of the other to connect/post to the "other side", think of them as translators so that the functionality is largely there, but there may be a few extra glitches here and there: you can view kbin instances from lemmy, for example, but only the posts that come after a user from the Lemmy instances subscribes to a Kbin magazine, or vice versa.

Subreddits = Communities (Lemmy) = Magazines (Kbin)