Do you ever ask them on a scale of 1 to 10, how likely are they to refer your lawn care business to a friend or family member?
If you ask the customer face to face, you get a chance to hear their feedback that they wouldn't share with you on a paper lawn care survey. If they tell you a number that is not too high, ask them why and try your best to resolve that issue.
If they give you a number that is a 10, why not then follow up and ask them for a referral on the spot? Who would they like to refer to you?
Could they introduce you to them? If not, could they call them and let them know you are going to call? Lastly if not that, how can you get in touch with them?
Try this out and see what kinds of results you get.