1840, short for lobscouse "a sailor's stew made of meat, vegetables, and hardtack," of uncertain origin (compare loblolly); transferred sense of "native or inhabitant of Liverpool" (where the stew is a characteristic dish) is recorded from 1945. In reference to the regional dialect, from 1963. Related: Scouser (1959).
Lobscouse. A dish much eaten at sea, composed of salt beef, biscuit and onions, well peppered, and stewed together. [Grose, "Dictionary of the Vulgar Tongue," 1788]