Hi @bretaalstrom
welcome to the forum!
Unfortunately nothing like this is built into Webflow Memberships and there are some hurdles with the way you’ve set it up.
That said, here are some solutions…
Jetboost
Quickest & easiest:
If you’re adamant about leaving this on the Memberships account page, think about using the venerable Jetboost favoriting system.
Instead of the user “favoriting” the lesson, they are “completing” the lesson. Same functionality, different framing of the task 
This is a plug-n-play solution that’s free to use on webflow.io
sites.
It’s a quick & very popular solution in the Webflow community.
Webflow CMS
Little more effort, very flexible:
There are a lot of limitations to using the Memberships account page like you are.
The common approach is to move what you need over to the Webflow CMS.
It’s fairly simple to create some automation that does this for you in real-time whenever a new member is created or updated.
Once you have a unique CMS page per user, tracking “completed” lessons become trivial, you just track that in the CMS and it’s displayed to screen.
With this approach, you’ve also removed a lot of the limitations for the features you’ll most likely need to add in the future.
Memberstack
Not what you’re asking for, but very flexible:
Webflow Memberships has a bunch of advantages that Memberstack does not, but… the big one Webflow is missing (right now) is flexibility.
Webflow Memberships has a very limited feature set right now, and it’s also not ready for a live site.
I’ve gone through several days of Webflow Membership API calls not working and invite emails not being sent.
It truly is in Beta, but will improve with time.
If you need a solid alternative today, Memberstack is popular with the Webflow community.
Here is an example course site I built with Webflow + Memberstack that does exactly what you’re asking for.
Signup with a fake email address and use the checkboxes to mark each lesson completed.
I’ve also created a step-by-step screencast that walks you through how I built this (along with the checkboxes):
Hope that helps!