Nice! It'll be a pain in the ass to get going, but as long as you sell yourself (not like that!) to your customers than they should have no problem helping you out with a good reference.
Heres how: Do a good job on the lawn
Make "friends" with your potential clients
Ask them in a non pushy way "it would reaaaaly HELP ME OUT" if you could give me list of 10 friends or family that have lawns! Maybe call 1 or 2 of them right now?

give it a try and I'll bet you can pull it off!