It simply can’t really happen due to the technical way Mastodon and Lemmy function. I’m not sure if there is a way to address this on either side (or if the developers would be willing to do so even if there was).
Mastodon needs to implement group support, you can follow the issue here (don’t get your hopes up though).
Yeah, I’m not going to defend Mastodon’s frankly bizarre Like system. It’s not even a privacy thing as favourites are fully public.