The name recalls the Laurenzergrund, a small suburb named after nuns of St Lawrence.
The lane was named in 1862 to preserve the name of the Laurenzergrund, a small suburb that grew around a farm of nuns who in 1533 joined the Laurenzerinnen, the nuns of St Lawrence. Its seal showed a gridiron, the saint's emblem; in 1904 it was one basis for the coat of arms of the Margareten district.