Unfortunately what you want to do would be very complicated to do. The lesson code was not written to be extensible. So there would be a lot of places in the code to change to add a new pagetype.
This not like the question bank which was constructed from the beginning to allow new question types, new behaviours or new import formats to be added as plugins. There is no plugins for the lesson module and pagetypes are not plugins.
Good developer skills and a good knowledge and understanding of the code of the lesson module would be needed to do that and it would be a task requiring a good amount of work.