What punishment will Buddhist laymen get for breaking the precepts?

If you break the precepts, you repent. The purpose of repentance is not to repeat it in the future.

As for punishment, I can't say what punishment it is.

It's often said very well

Everything you do has a cause and effect. What you have done and paid can't be called punishment, but it's just returned to you.

In other words, whether you are a Buddhist disciple or not, it is all the same, and there is cause and effect when you do it.

But through your practice, cause and effect can also be changed.