Customer said he wasn't going to pay us for the rest of the job. Can we file a lien?

Customer requests: SCOPE OF WORK INSTALL PVC FASCIA BOARD GARAGE AND PAINT CREAM COLOR SCOPE OF WORK $4,570.86 PAINT ALL COLUMNS THE SAME COLOR BEFORE AND REPAIR THEM IF NEEDED INSTALL 8 PC NEW SHUTTERS FRONT REPAIR BACK PATIO ROOF All of which was completed, signed contract, and paid deposit. The only thing that was not completed was the shutters. which came in the order late, we offered to have the shutters replaced despite the late delivery. The customer said he does not want us, even the owner to come back and finish the job. Customer said to the owner directly that he wasn't paying him anything. The owner was willing to go out and rectify the situation himself after the Installer completed everything else but complained about water damage that he was not willing to show proof of. All materials already spent money on and the installer paid. The owner was going to come to finish the job with no additional fees, restocking fee waived late fee waived, and no cost for the shutters, but the owner is refusing to pay for anything more beyond the deposit. Even though we were willing to adjust the total to reflect any material and installation requested for us not to finish. The customer was sent multiple emails requesting payment and was offered many different ways in which he could pay but now this money that is owed is affecting our operations.