Yeah, I'm pretty sure they interpret the endpoints differently so unless a mastodon post is directly targeted at a community or something, lemmy just drops it. That's why I still run a dedicated mastodon and lemmy instance. Kbin promises best of both worlds but doesn't seem mature enough for my tastes.
Generally if you search for the full URL or handle of a profile or community your server should be able to find it. For example to find a user like mark ruffalo I just searched for @MarkRuffalo@mastodon.social on my lemmy instance. After a few tries it did find him but not his posts. I've only reliably gotten this searching to work through the main lemmy ui so your mileage may vary depending on the app you use. Misskey should work similarly I believe but I don't follow or know of anyone on there so not sure