The Tony winning duo will explore Mamet’s comedy about two actors at different stages of their careers for Symphony Space.
Also featuring Waites' band Heartbreak Waites, Lucky Man–A Warrior’s Journey will play a strictly limited engagement this June.
Les Waters is directing the new work, back on after a strike postponed the original run.
Nick Hern Books will publish the work while it makes a bow at London's National.
The Doug Wright play is headed to the West End's Barbican Theatre this summer.
The spring All Arts lineup will also include the return of the talk show Broadway Sandwich and a documentary about the Palace Theatre.
Darren Criss, Helen J Shen, and Dez Duron entertained audiences at the Belasco Theatre when the April 22 performance was forced to pause.
The critically acclaimed Japanese cast, who toured the show earlier this year, will take the stage in London for one week only.
Michael Poore's cult favorite fantasy novel has been musicalized by Jukebox the Ghost's Ben Thornewill, BTS songwriter Coyle Girelli, and playwright Laura Zlatos.