He cannot validly file a lien on this property. If he does you will have a lawsuit against him and you will be able to recover a minimum of $10000 for filing a false lien. Verbal agreements are enforceable if they can be performed within one year. Proving the terms of a verbal agreement often is a swearing match between the two parties. Emails and witnesses could become very valuable. Retain them. You mentioned phone calls but no written notice or demand to complete. See a lawyer and have him/her prepare that notice and demand. Then when the time for responding has expired, you can hire someone to complete the work and offset that cost against what you owe the original contractor.
DISCLAIMER: This is not specific legal advice and does not establish an attorney/client relationship.