When it closes, the production will have played a total of 102 performances.
Burstyn is expected to bring the one-man show to Florida audiences later this year.
Penned by Joseph Bologna and Richard Krevolin, Lansky features direction by Bologna.
Burstyn previously starred in the play at the Odyssey Theatre in Los Angeles in summer 2008.
Inspired by the book "But He Was Good To His Mother" by Robert Rockaway, Lansky, according to press notes, "imagines the notorious businessman and gangster, who masterminded some of the most ingenious wealth managements systems of his day, struggling to reconcile his material successes with his desire to gain Israeli citizenship, live out his days in the Promised Land and ultimately be buried next to his beloved grandfather in Jerusalem. With brutal honesty he subjects himself to an unsparing first degree in which he asks himself if his pursuit of the American dream and first-generation assimilation in this culture are worth the price he paid, and, more profoundly, if it is possible for him to be a good Jew and also a good American." The production features set design by Josh Iacovelli, sound design by David Beaudry, lighting by Graham Kindred and costumes by Cyona Burstyn.
Mike Burstyn has been seen on Broadway in The Megilla of Itzik Manger, Barnum and Ain't Broadway Grand. He received a Drama Desk nomination for his performance in On Second Avenue, and his other theatrical credits include Jolson, The Rothschilds (Drama Desk nomination) and The Tale of the Allergist's Wife. Burstyn is also the recipient of three Israeli "Oscars."
Bologna is also the author of Made for Each Other and Lovers & Other Strangers, both penned with wife Renee Taylor. Krevolin also wrote the hit comedy King Levine.
St. Luke's Theatre is located at 308 W. 46th Street. For tickets, priced $31.50-$56.50, call (212) 239-6200 or visit www.telecharge.com.