You need to file a formal answer in response that admits, denies, or denies knowledge or information sufficient to form a belief as to the truth of each of the numbered paragraphs in the complaint, and you need to assert all affirmative defenses or counterclaims in your answer too or else you may waive (forfeit) the right to assert them later. A notarized letter is generally unacceptable for this purpose. I recommend going to the Pro Se Office in the courthouse to obtain more information, but if you can't afford a lawyer, I'm afraid that you are not very likely to defeat this lawsuit. New York's Lien Law is not easy to understand or intuitive, and you could easily end up losing your lien (and with it, the right to collect). On the other hand, if you have all the backup documentation and/or if it's a large/valuable lien, you may be able to find a lawyer to do this litigation on a partial contingency basis. Obviously, you need to move quickly, but your best bet may be to go to court on 5/21 to ask for time to hire a private attorney. If you can't get one, then it may be worth trying to settle the lien with the other side, even if you only get 10-15 cents on the dollar, since that's more than you will get if the lien is cancelled (but it probably works out to less than the attorney's fees they will need to pay in order to litigate this case).
It entirely depends upon what the Order to Show Cause seeks. If they are seeking to cancel a mechanic's lien it could be under Lien Law Section 59, Section 19 or something else. You must consult with a local construction attorney about the specifics of your case. If you are a corporation or an LLC you cannot respond to the Order to Show Cause yourself you must hire an attorney to do so.
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.