What do you think about this sentence?
Do you have bought the lesson book?
Is that a correct usage of "Do you have bought"? Or should I say "Did you buy"?
As written, your sentence is not grammatically correct. In order to use the Present Perfect, you should say:
Have you bought the lesson book?
You are trying to ask if someone has bought the book, so the verb "to buy" needs to be in the right tense. You could also write,
You have bought the lesson book?
But starting the sentence with "have" is a valid use of inversion in English, which denotes a question. "Do" does not add anything to the sentence, and is not part of the present perfect tense.
Now, should you use the Present Perfect here? You definitely can, because present perfect can denote the concept of unspecified time. You are not sure when or even if the person bought the book, so you are trying to figure that out by asking "have you..."