The alley next to La Mama is called Extra Place. It was hardly recognizable as an alley until recently, when part of the Avalon Bay conglomerate of buildings went up next door. Its been re-branded and architecturally rendered as a pedestrian mall, though only bits and bobs have come to fruition. Check out this piece for the Huffington Post about Extra Place by Kevin Walsh, the creator of Forgotten New York. Thanks to Bowery Boogie for posting this picture from the Forgotten NY website, its made me do a bit of digging.
Forgotten NY website.