I'll offer two reactions:

As a customer I am not bothered at all if front desk staff choose not to wear lipstick. I certainly always appreciate a professional appearance, including matching uniforms that fit and are kept neat and clean, well groomed hair, and good personal hygiene. Makeup is not really a part of that to me-- except as a negative, when it's applied poorly (often when used excessively). More important to me than any appearance issues, though, are the staff's professional behavior and competence.

As a business savvy person I am bothered that your client thinks it's okay to add arbitrary requirements not documented in your contract. That is not professional. Call them on it!