The mass-market beauty company had $96.8 million in sales for the first half of 2016.
Rights groups applaud the decision as a victory for individual and religious freedom.
Incoming president Mario Grauso will assume the chief merchant role.
The mirror records images and videos of the customer, letting them compare side-by-side images of them wearing sunglasses.
The in-store boutique will open in Los Angeles, Nashville and Toronto.
The relaunch includes improved navigation and a more “responsive design” as well as one-page checkout.