National Football League-backed play “Lombardi” has become the first Broadway production to announce its closing in the wake of the Tony noms, with the gridiron bio set to shutter May 22.Open-ended run of the show about coach Vince Lombardi, portrayed by Dan Lauria, earned a single Tony nod for thesp Judith Light, who appears as Lombardi’s wife. But news wasn’t enough to boost optimism about the play’s B.O. prospects. Weekly sales have generally been modest but steady since the production opened Oct. 21, although in recent frames receipts have consistently landed in the $200,000 range and last week slipped to $155,898. Production boasted an unusual deal with the NFL, which contributed its considerable marketing muscle to pushing the show during the Super Bowl and other NFL events. The org also allowed “Lombardi” to use NFL archival footage in the show and brought in memorabilia to be displayed in the theater’s lobby. Such efforts targeted male sports fans, a group well outside what is considered the traditional theatergoing demo. Production is not expected to recoup before it shutters, according to Fran Kirmser, who produces with Tony Ponturo. Still, the pair expect future revenue from licensed productions of the title, with rights available through Dramatists Play Service. Kirmser said a number of theaters around the country already had expressed interest in staging the show. Kirmser and Ponturo aim to tap another sports-legit synergy with “Magic/Bird,” a new play based on the lives and rivalry of hoops stars Magic Johnson and Larry Bird. New play targets a spring 2012 opening.