There is a similar topic on beehaw.

Yes, lemmy posts can be indexed and found, but there are disadvantages compared to big, centralized services. I just found some posts on ecosia page 3.

I’m not sure if posts from instances without ‘lemmy’ in their name would show up when somebody searches for “something lemmy”.

Yes, actually it’s already getting indexed. For example you can try searching for site:lemmy.ml on DDG or Google. Although it’ll probably take a while before search engines will deem lemmy instances “popular enough” for posts to show up for regular search queries (assuming that’ll even happen at all).

They aren’t behind any login or anything stopping it. So yah, I expect they’re already are being indexed.