I have reported that "He is sleeping in the lesson." should be accepted. Hmm, you'd have to check with one of the mods, but I -think- "under" would be right but possibly have more of a suggestion of TIME, rather than PLACE. I take it from this sentence that there is a student or teacher sitting in the classroom, asleep. I would IMAGINE that "Han sover under lektionen." could suggest that maybe he is at home sleeping while he should be in class. But again, ask a mod or a native speaker.