I started a job and had a few delays the customer doesn't want me to finish do I owe them a refund
This is a contract question - not so much a "construction" issue. That said, the answer depends on 2 things:
#1 The terms of your Contract
#2 Law in your jurisdiction (most likely, the Uniform Commercial Code)
The general rule applicable to conracts is that if you do work at the request of a customer and they "cancel" without a valid basis, that is a breach. You were ready to do the work, but they backed out. In that case, you are entitled to what you would have made had you done the job (which you were prepared to do).
In addition. you are entitled to the value of any custom-made materials, and for the value of the work in place. This is where a Mechanics Lien comes into play: Illinois law convey on you a lien right equal to the value that you added to the property.
I hope this information was helpful. Best of luck!