3 letter .net, .org, .com, and probably most of the more esoteric domains are gone. same goes for 4 letter domains.
Re: .nets, in general, in almost all circumstances, I don't recommend using a domain extension that requires further explanation of how to find your business. When people ask for your domain, especially a long one, having to then say, "Oh, and it's .net, not .com." creates a headache that could lose you that visitor.
In this situation, I'd go with Greg's suggestion and register the full name. For signage, you can capitalize and have a color variation to further aid quick readability.
Side note: To me, lawn care businesses should be looked at as any other business. When you are coming up with a name for your business, a trip to your favorite web registrar (namecheap, godaddy, etc) to check availability should be your first or second step.