In addition to being filed way too late, the lien also appears to be defective because the owner of the property (you) did not consent to the work or agree to be responsible for any payment. Lack of consent for the work defeats the lien. It sounds like you have a number of problems and will likely need an attorney to remove the lien as the process for lien removal in New York can be very complex.
The information provided herein is for informational purposes only and does not constitute legal advice. No attorney-client relationship is created by this answer. You should consult with a local attorney regarding your specific situation to obtain legal advice.
You have a problem. The lien shouldn't have been filed this long after the work was done. You need to share the actual paper work with a local attorney to get this resolved. If you do nothing, the lien holder will have to bring suit against you. That would be more costly than getting it straightened out with your own attorney now before law suits begin.
Please remember that this is free advice given on a very limited amount of information. You can't rely upon it, or impose an attorney client relationship on me without retaining my services.