We currently have users who sell virtual courses based on their ACL levels (each course is accessible based on the Joomla User Group) and then using the Add To User Group app, you could sell each course and set the user group(s) the customer is added to based on their purchase.  

This is at the most basic level. If you are looking for something more similar to an LMS, you could still use J2Commerce to handle the ecommerce side of things and using the same app mentioned above add them to whichever user group the course is set to. Each LMS is different so you may need some customization to make it work seamlessly depending on which system you use, but based on your last question above, the answer is yes - you can use it to do exactly that without any additional modifications.

We are also in the beta testing phase of the Subscriptions and Memberships app which would allow you to add/remove them from those user groups when they pay/renew a subscription or cancel it which would add a powerful recurring income stream to the process.

Hope this helps!

Adam