Oh...thanks for the info as I am not yet up to speed on your sitch. Yeah, best to stick with L's advice. Sorry you're going through this.
For what it's worth, you DO have control of your L. When I got my own L, I made my instructions very clear to her: be respectful and have integrity in their interactions with the other team. You're the boss and you hired the L. If L cannot accommodate you, then find another one who fits your needs the best possible way.
