I am a subcontractor on a public project in NYC that is still on going, the job has had no movement in months and we are owed a substantial amount on monies. a notice of intent to lien has already been sent to the GC.
Since the public owner has not accepted and closed out the job, you can just file the lien with the public owner and (usually) the Comptroller's office. You do not need to file a "pre-lien" document like you have to in other states.