He had already been reprimanded for this behavior at school. He also realizes that it was wrong to do so and that you were upset because of it.
At this point, it may be helpful to sit down with him and try to find out what is going on with him. There may be external factors causing this dishonesty such as: peer pressure, conflict w/teachers, fear of being punished at home, etc.
Even if the behavior is undesirable/unhealthy, it still serves some purpose to him. Perhaps you can try to figure out what that is. Is he lying in order to look better to others (if the lie is believed) is he doing it to cover up for someone else, is it for attention, to relieve anxiety
, poor problem solving,etc.
When you speak to him, you may point out to him that lying reflects negative on him but in the end, he is in a way cheating himself. You can then explain to him why it is better to address things that may even be problematic or scary rather than pretend that they're not happening or to lie about them.
He could write down what had transpired and then speak to you about it if he's uncomfortable/scared to just talk. He may write down what happened in reality, what he said happened (the lies), why he did
that (what motivated him to do it) and what could of been done differently all together. He may have been focused on the immediate "solution" to the problems that caused his dishonesty rather than think about how lying can cause a whole lot of other outcomes.