N.Y. Lien Law § 62
A lienor who has filed a notice of lien after the commencement of an action in a court of record to foreclose or enforce a mechanic's lien against real property or a public improvement, may at any time up to and including the day preceding the day on which the trial of such action is commenced, make application upon notice to the plaintiff or his attorney in such action, to be made a party therein. Upon good cause shown, the court must order such lienor to be brought in by amendment. If the application is made by any other party in said action to make such lienor or other person a party, the court may in its discretion direct such lienor or other person to be brought in by like amendment. The order to be entered on such application shall provide the time for and manner of serving the pleading of such additional lienor or other person and shall direct that the pleadings, papers and proceedings of the other several parties in such action, shall be deemed amended, so as not to require the making or serving of papers other than said order to effectuate such amendment, and shall further provide that the allegations in the answer of such additional lienor or other person shall, for the purposes of the action, be deemed denied by the other parties therein. The action shall be so conducted by the court as not to cause substantially any delay in the trial thereof. The bringing in of such additional lienor or other person shall be without prejudice to the proceedings had, and if the action be on the calendar of the court, same shall retain its place on such calendar without the necessity of serving a new note of issue and new notices of trial.
N.Y. Lien Law § 62