Is it possible to add quiz to the lesson of the HTML type? So that I could read the text and answer questions immediately.
(you can do it for example, in edx)

I can't understand. You have WYSIWYG editor ( = HTML) for test description, for each question and for each answer.

I think the user doesn't want to use the "test" LO but the HTML page LO and turn it to a test. At least that is what I understood.

Yes, but my question for him is: WHY if... ?

Oh, well, many of the questions that people post on the forum would need a big WHY...