If you think users will notice the difference between https://learing.com/forum/ and https://forum.learning.com , you can Serve Discourse from a subfolder (path prefix) instead of a subdomain.
You can also Embed Discourse comments on another website via Javascript. That will display some discussion on the page, but take users to Discourse to interact with the forum. That’s probably what I would recommend.
If what you want is the problem and the forum on the same page as other LMS stuff (which I don’t remember seeing in any of the LMSs that I have used), it’s possible to embed Discourse in an iframe (though it hasn’t always been the case, and it’s not well documented; there is a hidden site setting allow_embedding_site_in_an_iframe).