O.E. læfan "to let remain, remain, bequeath," from P.Gmc. *laibijan (cf. O.Fris. leva "to leave," O.S. farlebid "left over"), causative of *liban "remain," (cf. O.E. belifan, Ger. bleiben, Goth. bileiban "to remain"), from root *laf- "remnant, what remains" (see life, live), from PIE *lip-/*leip-. The Gmc. root has only the sense "remain, continue," which also is in Gk. lipares "persevering, importunate." But this usually is regarded as a development from the primary PIE sense of "adhere, be sticky" (cf. Lith. lipti, O.C.S. lipet "to adhere," Gk. lipos "grease," Skt. rip-/lip- "to smear, adhere to." Seemingly contradictory meaning of "depart" (early 13c.) comes from notion of "to leave behind" (as in to leave the earth "to die;" to leave the field "retreat").
"permission," O.E. leafe, dat./acc. of leaf "permission," from W.Gmc. *lauba, cognate with O.E. lief "dear," the original idea being "approval resulting from pleasure." See also love, believe. In military sense, it is attested from 1771.