Is it safe to put lidocaine on female genitalia? Will is cause a numbing affect?

Yes. Yes it is safe when used properly. I have prescribed topical Lidocaine for the relief of primary or episodic herpetic lesion pain.
What for? If a woman were to want to use a numbing cream because sex is painful, i'd want to look further into the reason. Many women in the 'perimenopause' will experience vaginal dryness as their estrogen production decreases. There are lubricants and hormone medications that can be helpful. I would be concerned that numbing the vagina might permit you to be injured without being aware of it! talk to doc.