Old English lamb, lomb, Northumbrian lemb "lamb," from Proto-Germanic *lambaz (source also of Old Norse, Old Saxon, Old Frisian, Gothic lamb, Middle Dutch, Dutch lam, Middle High German lamp, German Lamm "lamb"). Common to the Germanic languages, but with no certain cognates outside them. The -b has probably been silent since 13c.
The Old English plural was sometimes lambru. A symbol of Christ (Lamb of God), typified by the paschal lamb, from late Old English. Applied to gentle or innocent persons (especially young Church members) from late Old English; from mid-15c. of persons easy to cheat ("fleece"). Also sometimes used ironically for cruel or rough characters (such as Kirke's Lambs in Monmouth's rebellion, 1684-86, "an ironical allusion to the device of the Paschal Lamb on their flag" [OED]); Farmer and Henley ("Slang and Its Analogues") say "specifically applied to Nottingham roughs, and hence to bludgeon men at elections." Diminutive form lambie is attested from 1718. Lamb's-wool is from 1550s as a noun, 1825 (also lambswool) as an adjective.
Watkins suggests it is perhaps from PIE root *teue- "to swell," but Beekes writes that it is probably a Pre-Greek (non-IE) word. He writes that Latin tumulus "earth-hill" and Armenian t'umb "landfill, earthen wall" "may contain the same Pre-Greek/Mediterranean word," and suggests further connections to Middle Irish tomm "small hill," Middle Welsh tom "dung, mound."
The final -b began to be silent about the time of the spelling shift (compare lamb, dumb). Modern French tombeau is from Vulgar Latin diminutive *tumbellus. The Tombs, slang for "New York City prison" is recorded from 1840.