He cried and said he didn't even realise he was being rude
He's very upset the teacher thinks he is a rude child now and wants to say sorry
This reinforces the point I made earlier in the thread. Your DS sounds very like a child who is not clued up to social norms and is struggling in school.
Lots of children on the autism spectrum speak to teachers in the same way they would speak to their friends because they genuinely don't understand that it is socially unacceptable. Some children aren't able to pick up these rules instinctively and need someone to explain them carefully. It's not an easy task.
Please, please don't punish him. Try to work out what else he might be struggling with, e.g. having to sit still might be making it hard for him to listen. He is clearly struggling socially as he doesn't know how to interact with his peers. He finds it hard to concentrate in class which could be for all sorts of reasons e.g. sensory processing, executive function (organising his thoughts and following complex instructions), central coherence (seeing the bigger picture rather than lots of minor details).
He might not be bothered about losing lunchtimes because he finds it socially overwhelming and hard work or possibly because he is emotionally immature and can only identify with the emotions he is feeling in the moment.
You cannot manage behaviour successfully unless you understand the reasons behind it. I think there could well be some reasons behind your DS's behaviour that nobody has cottoned onto yet. Teachers don't always spot subtler difficulties because they aren't trained to.
If he is struggling in school then comes home to more punishment and criticism, his self esteem is likely to plummet and he will struggle more.
I'm not saying your DS has ASD but he could have some of the difficulties experienced by children who are on the spectrum and, if he has, punishing him is the very worst thing you could do.
This behaviour would definitely bear further investigation.