Many customers use LMS plugins in conjunction with MemberMouse to offer a more robust online experience for the customer, while still protecting lesson pages using MemberMouse's content access protection functionality.
Here are a few LMS systems that customers have used:
WP Courseware has developed a plugin that integrates their software with MemberMouse. You can download their plugin here: https://wordpress.org/plugins/membermouse-addon-for-wp-courseware/
There are other LMSs out there to use. As long as your LMS uses a custom post type (which most do) there should not be an issue using MemberMouse along site your LMS of choice.
One thing to remember, most LMS driven websites are set up to allow customers to purchase the courses a la cart, meaning they can pick and choose what they want to purchase. Because of this, you will want to be sure to become familiar with how to use MemberMouse bundles, which are different than membership levels. Bundles allow customers to purchase multiple unique courses, and keep them all active at the same time.