Different sites can have different plugins enabled, different sets of users, etc. That’s built in to Multisite.
The “LMS talking to ecommerce” part will probably require you (or someone you hire) to write some code — a head start might be to look at switch_to_blog() and restore_current_blog(), and indeed the list of Multisite functions. (Or you can enable the ecommerce plugin on the LMS site as well.)
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