What dose "if you may."mean?
Lion: I got something stuck in my teeth. It's driving me crazy! Can you help me out here? Please?

Zebra: You came to the right place, my friend.Doctor Marty D.D.S. is in the house!
Please hop on top of my sterilized examination table, if you may.

I picked up this dialogue from the first scene of anime Madagascar1
Dose "If you may" is complete sentence or,,?
thank you♪

Question

What dose "if you may."mean?
Lion:  I got something stuck in my teeth. It's driving me crazy! Can you help me out here?  Please?

Zebra: You came to the right place, my friend.Doctor Marty D.D.S. is in the house!
            Please hop on top of my sterilized examination table, if you may.

I picked up this dialogue from the first scene of anime Madagascar1 
Dose "If you may" is complete sentence or,,?
thank you♪

Answer

It's not a complete sentence.  It's a formal, polite phrase which means "please", "if you don't mind".