Do I need my own e-money license or can I start under a leased license?

If you’re going to be a financial intermediary (for purposes of money transfer/remittance business), chances are you will be classified as a Money Services Business and hence would require a money transmitter license in each state you operate in.

You can absolutely do the on the sponsorship program with an existing license holder or a chartered bank/credit union if they will cover you. In which case, you will not be needing to go through the rigorous process of applying for licenses, getting your net worth to the minimum levels required, surety bonding, compliance, audits, personnel, etc.

The leased route as you put it is definitely the way to go.

Here is a rough estimate of how much money it costs and how much you will save.

Money Transmitter License Cost: Own vs. Sponsor? - Faisal Khan