"Could I hand in the lessons that are late" is fine. And so is "Could I hand in the late lessons." You could also say "Can I hand in the past-due assignments/lessons," as well.

Sorry, but it isn't clear what the situation is. None of those sentences make sense, because you cannot 'hand' a 'lesson'. This does not mean anything. Are you talking about lessons ('aulas' in Portuguese), or are you talking about pieces of written work (for example essays that you have written)? If you are talking about pieces of written work, the verb is 'hand in'. For example, if you should have handed in your essay last week, you can say something like 'Can I hand in my homework late?' or 'Can I hand in my overdue essay?'