OP, I highly doubt you will be able to just add your name to the lease agreement to start building your credit, lender's don't typically change contractual agreements mid-way through a loan to add someone to it.
In fact, If your friend financed/leased this vehicle in only their name for your purposes of driving and paying the payment, I would avoid informing the lender of this, as it was a "straw-purchase"
Straw purchases are when a person finances a vehicle for someone else's use, with the intent that they are making the payment and not the actual debtor. It is a big no-no in the banking/lending world and most bank's prohibit it.
When does your lease end? if it is relativley soon then I would start preparing your credit in order to release a vehicle or finance a vehicle directly afterward's with a co-signer if you need it. Get some credit card's, and maybe a small installment loan to build your credit.
