I think lunch or other get togethers are fine with an EX Therapist. So is asking not to share her Facebook, phone number, etc with others is also okay in my opinion. But if someone tells me I have to hide things from others, short of a surprise party, I would object strenuously. Her request is strange to me.

I have done all sorts of things with my ex therapist which includes joining her family for Christmas dinner last month. She is/was the therapist for other people I know and she has never asked me to be secret about our friendship.