LMTP is a small modification of SMTP with a per-recipient response code - but I'm not sure what it's intended for. It isn't used on the internet. It's sometimes used as IPC within a mail server.
LMTP is for delivering to an IMAP (or JMAP) mailbox, generally. We also have a plugin for that. But it has certain flaws for exposing it to the internet (I just forget what they are right now).