No, If you have a membership site then only Memberpress is all you need. It will ensure only appropriate users can access exclusive contents on your website.
However, If you want to add some courses, quizzes, certificates into your membership site, you will need LearnDash.
NOTE: For only learning website, you actually do not need a membership plugin for content protection. This LMS will protect your content without the need for a membership plugin using its Access Settings.