Nickname for a fleet-footed or timid person, from Old French levre "hare" (Latin lepus, genitive leporis). It may also have been a metonymic occupational name for a hunter of hares.
Topographic name for someone who lived in a place thickly grown with rushes, from Old English lǣfer "rush, reed". Compare Laver. Great and Little Lever in Greater Manchester (formerly in Lancashire) are named with this word, and in some cases the surname may also be derived from these places.