Hey Ben and welcome back!
Interesting use cases. I do believe our plugins will work here.
For example, The Events Calendar (free) can handle the load of lectures and classes that should not be bookable. You can use event categories to categorize the events as Lectures and Classes.
For the events that are bookable, then you might want to consider Eventbrite Tickets. That would allow you to publish your events on Eventbrite.com, import them into WordPress to The Events Calendar, show tickets for those events, then handle the payments completely offsite on Eventbrite.com.
Another way to do it would be to nix Eventbrite Tickets and simply use the Website URL field in the events editor to link directly to the platform you are using to take payments. In other words, you may be able to get away with only the free version of The Events Calendar and nothing else.
Would either of those options work for you? Please let me know. 🙂
Cheers,
Geoff