I assume that your connection is from one international flight to another international flightl?

I think the easiest way - by far - for you to do this will be to accept the relatively small costs of withdrawing a couple of thousand yen from an ATM to buy your train ticket and pay for a coin locker.

If you want to avoid withdrawing cash, I don't think you can buy a ticket for the local Keisei train. [Keisei's website states that cards can be used for the express trains into Tokyo, but does not mention card use for local trains:
http://www.keisei.co.jp/keisei/tetud...ket/index.html
Someone will correct me if this situation has changed. It's not something I have looked into recently. The local Keisei train is the easiest and most frequently running connection to Narita City. Avoiding it because of an ATM fee seems short-sighted.

If you are really desperate to get to Narita free of charge, you might be able to finagle your way onto a shuttle bus to a hotel in downtown Narita [But be careful because most hotels are not in town - you'll need to choose carefully]. The shuttle buses are intended for hotel guests, so this requires more chutzpah and less honesty than I could muster.

It's probably physically possible to avoid spending money on a coin locker by leaving your luggage in the lounge, but it's in breach of security rules. You'll hear lots of announcements not to leave luggage unattended in the airport - and I have a feeling that leaving the bag in the lounge and going landside would be frowned on. Best not to mess around like that IMHO. Also, it's just not a very convenient thing to do for the sake of saving a few hundred yen. You would need to go through transit security to get to the lounge, and then ask directions to exit the gate area and go through whatever route exists to take you to the immigration counters so that you can go landside. My advice - if you really can't afford a locker - is to travel light and haul your cabin luggage with you around Narita.

I can understand not wanting any yen left over. You could get rid of any leftover coins at a store in the gate area (use up your remaining cash and pay the balance with a card). Or you could donate them to charity.