I'm in the dark --- why ever would you NOT want to tell her the truth?

You could write her a short note detailing your reasons for making a change. She needs to know that if she isn't keeping up with the latest techniques she will lose her bread and butter. This will take more time on your part but help you avoid confronting her.

Or --- just phone her and politely cancel your next date, say you want to discontinue your standing appointment, and say good-bye.