Transferred use of the mainly Scottish surname, in origin a local name for someone who came ‘from the island’ (Anglo-Norman de l'isle). (The island in question would in many cases have been an area of higher, dry ground in a marsh or fen, rather than in a sea or river.) There may have been some confusion with Lyall.
German: metonymic occupational name for a shepherd, from Middle High German schāf ‘sheep’. In some cases it may have been a nickname for someone thought to resemble a sheep, or a habitational name for someone living at a house distinguished by the sign of a sheep. Compare Schaap.