To directly answer your question, a mechanic's lien under New York law cannot be placed for work that has not yet been done. A mechanic's lien may only be filed for labor and materials actually performed and delivered (with the exception of specially fabricated materials).
If your demand for an itemized statement has not been responded to, then, assuming you have properly served it, you may initiate a special proceeding seeking the itemization under Lien Law section 38. If the order to compel is not complied with then the lien can be discharged by further order of the Court.
You should contact a construction attorney to discuss the specific details of your situation. The Lien Law can be very difficult to understand even for lawyers so make sure you find someone experienced with construction law, and specifically the Lien Law.
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.
A lien will tie up your property. You should hire a local attorney to negotiate and take care of the lien and ensure the terms of the contract are performed.