Oh dear, I can feel the frustration in your letter.
People do not change overnight unless something has occurred and, in this case, cause a negative effect. You mentioned that you have noticed the change in your friend over the past eight months. Something might have happened in L’s life to cause such a change in her attitude? It may not be obvious to you, so think deep. Has L mentioned anything to you that you have forgotten or could she be dealing with something that is very sensitive and difficult to discuss?
I would also like you to reflect on the past eight months with regards to yourself and ask if it is only L that has changed or has something happened in your life that has made you less tolerant of your friend?
Putting this aside, rudeness and humiliation is not to be tolerated and you did the right thing with regards to addressing this issue with her.
Cutting ties with a long-lasting close friend is going to be difficult no matter how hard you try to make it amicable. L knows you as much as you her. She will know that there is a change in dynamics with your friendship but will not necessarily believe that her insolent manner is the cause of it. Again, you did the right thing in attempting to discuss the occurring problems with L. Unfortunately, L is hiding from the truth and either will not accept what you have to say or just does not want to hear it. My advice is to write to her and let her know how you are feeling. As you will not be there when she is reading your letter, L will not have the opportunity to ‘jump down your throat’ and as a result will hopefully take in the contents and what you have to say.
In your letter, explain to L how she made you feel in the restaurant and what the consequences of her actions were. Also, inform her that you do not want to be in that environment and that her change in temperament has had a serious impact on your friendship. You could also take this opportunity to ask L if anything has happened to make things change and offer her the chance to talk to you about it. You may be surprised. However, make it clear that you will not tolerate any more uncomfortable situations.
All your answers will be in L’s response to your letter. She may be genuinely sorry and want to make amends in which case give her the benefit of the doubt. There may be an underlying reason which is the root of this situation. Or, L may feel the same and want to cut ties as well and is acting this way to drive you away.
True friendship is built on trust and respect for one another. If L does not appreciate your letter, then I would suggest that you move on without her. As sorry a situation that this will be it does take both parties to want to do it and you have tried.