Right, that answer should be accepted. I would also argue that lately not is not even grammatically correct but that's just the teacher in me. Make sure you report this!
I agree, 'not lately' sounds better. But 'lately, no' is accepted and I can perhaps imagine saying it in a conversation. 'Have you been going to your exercise class?' "Lately, no." to emphasise that it's only lately that I've not attended.