What’s the best way to track referrals for course enrollments like with an affiliate program?

LifterLMS is affiliate ready. AffiliateWP has added direct integration with LifterLMS to track referrals. You would need to install the AffiliateWP plugin to launch your affiliate or referral program on your LifterLMS website. iDevAffiliate and WP Affiliate Manager also work with LifterLMS.