Are they all natural? As I understand it, the second one is more common, because there's a question about timetable. But the third one isn't correct because of classes are not a personal arrangement. Right?
How many lessons/classes will you have tomorrow?
How many lessons/classes do you have tomorrow?
How many lessons/classes are you having tomorrow?
P.S. I have three grammar books and none of them doesn't contain information that Present Continous is used in any situations with timetable. It's from advanced grammar: "We can often use either the Present Simple or "will" to talk about future events that are part of some timetabled or programmed arrangement or routine."