I did a bunch of experiments today and ... thoroughly confused myself, so I wrote down a bunch of things and took screenshots.
Here's what I learned:
(I have more protocol info but ultimately this is the lived experience of working across different software systems, federation, and the actual client / front end web experiences that people interact through)
Paste Lemmy URLs
Various things "just work" by pasting URLs into the Mastodon web interface or the Mastodon mobile app.
Posting the link to this post https://lemmy.ca/post/606549 finds this post
Clicking on the user profile shows me a profile for Doctor_Pi@lemmy.ca, with one post displayed. Including a follow button
Only one post is shown, because that's all that's available on the local server right now. If I chose to follow Doctor_Pi's Lemmy account, I'd get all of their posts going forward. Both OPs (which has a link to the post on Lemmy.ca) as well as comments (which appear as replies).
Limited support on other clients
Other clients (Ivory on iOS) have extremely variable support. You can't usually paste in Lemmy URLs, but you can paste in Lemmy accounts and follow them, and then see posts going forward.
Please leave a comment of what does / doesn't work in your particular client.
Follow Lemmy users on Mastodon
Every Lemmy user can be followed on Mastodon. So, for example, my Lemmy account @boris@news.cosocial.ca. Paste that into the web interface of Mastodon or into the Mastodon native mobile app and you will find my Lemmy profile and can follow it.
Reply to a Lemmy post from Mastodon
If you reply to a Lemmy post using your Mastodon account, your reply will be posted as a comment. A user profile is created on the Lemmy instance.
I just did that with this very post, and it seems to have worked.
This is my boris@cosocial.ca Mastodon account, viewed through news.cosocial.ca as a local user profile. All of that info -- including the images -- are from my Mastodon profile.
The comment is technically originally on Lemmy.ca.
Create new OP post from Mastodon
You can create new OP posts directly from Mastodon. @-mention the group name, e.g. @vaneats@news.cosocial.ca.
I often share ("boost") lemmy posts on mastodon. I would like to be able to add hashtags to the boosted post, because on mastodon I rely on hashtags to find content that interests me (e.g. I follow certain hashtag. Lemmy doesn't need those because the general theme and topic is often obvious from the community context it was posted in, but this context is lost when sharing on mastodon. For example, when I post something in c/baduk@lemmy.ml, for lemmy users it will be clear that this post is about Baduk (the Korean name for the game of Go). But when I boost the post on my private mastodon, it's not obvious anymore that this was posted in a Baduk community and the Baduk-interested people on mastodon will never see the post except if they follow me or the lemmy comunity. All solutions that come to my mind seem a bit awkward, are there any best-practices for that?