O.E.
lim "limb, joint, main branch of a tree," from P.Gmc.
*limu- (cf. O.N.
limr "limb,"
lim "small branch of a tree"), a variant of
*liþu- (cf. O.E.
liþ, O.Fris.
lith, O.N.
liðr, Goth.
liþus "a limb;" with prefix
ga-, source of Ger.
glied "limb, member"), from PIE base
*lei- "to bend, be movable, be nimble." The parasitic
-b began to appear late 1500s for no reason. In O.E., M.E., and until lately in dial., it could mean "any visible body part."
"The lymmes of generacion were shewed manyfestly." [Caxton, "The subtyl historyes and fables of Esope, Auyan, Alfonce, and Poge," 1484]
Hence,
limb-lifter "fornicator" (1579). To
go out on a limb in figurative sense is from 1897.
Life and limb in ref. to the body inclusively is from c.1205.