I think OP is asking about a broader, Fediverse-scaled search. So using the site: search tag will only search a single Lemmy instance. I don't think Google will index cross-instance content in those searches, otherwise it'll end up with a ton of duplicate results. So if what you're looking for was actually posted to a different instance, it may not be found with that search.
I'm just theorizing, though, since this is all still really new and untested.