The “s” in “https” refers to how the server handles security. So you may have to change the address of the LMS, but it should access courses that are uploaded to it. If not, sit down with IT for a face to face. It sounds like you got an automated notification. Make sure they have implemented it, and why “http” works and “https” doesn’t.
The .html file that is produced by publishing doesn’t enter into the equation, so it doesn’t need to be changed. http://company.com/file.html and https://company.com/file.html are the same file, just think of them as living at different addresses.