What's your small-claims court where you live? Here an lco can file in small-claims and the debtor will be issued a summons,which they have to respond to or be cited for contempt. If a judgment is rendered against the debtor, the info will be picked up by the credit bureaus. This is generally much more costly than a measly mowing bill, so most people pay even before going to court.
In your situation, the weak point is whatever proof of your claim you can present to the court. Is there anything in writing? If you have copies of anything you sent, a copy of an estimate, even if not signed by the customer, that can help your case.
When I used small-claims, it always was to get money from a customer that I had a work history with, and I could present a record of work and payment prior to the work I did not get payment for. That was considered sufficient evidence that a verbal contract had existed.
I never had a written contract with a customer. That is quite rare in this area, except for large commercials, and landscaping installs.
You might just have to eat this one.