Did you acquire the phone from another user.....who was a customer of Verizon?
If the phone needs to be unlocked, Verizon will only do this for their customer.....and you are not the customer. The Verizon customer will likely need to contact Verizon and ask them to unlock the phone.
My neighbor's son bought a phone from another user only to find that the seller was many months behind in payments to the carrier, so the carrier would not unlock the phone for the original owner.....and they would not unlock it for the neighbor's son because he was not the customer. Of course, the original owner could not be found when the neighbor's son wanted to return the phone for a refund.
The bottom line.....things can get really messy when you buy a phone from another user. The fact that the seller might say that the phone is "paid off" and "unlocked" does not mean that this is true.