leave (v.) Look up leave at Dictionary.com
Old English læfan "to let remain; remain; have left; bequeath," from Proto-Germanic *laibijan (cognates: Old Frisian leva "to leave," Old Saxon farlebid "left over"), causative of *liban "remain," (source of Old English belifan, German bleiben, Gothic bileiban "to remain"), from root *laf- "remnant, what remains," from PIE *leip- "to stick, adhere;" also "fat."

The Germanic root has only the sense "remain, continue," which also is in Greek lipares "persevering, importunate." But this usually is regarded as a development from the primary PIE sense of "adhere, be sticky" (compare Lithuanian lipti, Old Church Slavonic lipet "to adhere," Greek lipos "grease," Sanskrit 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").
leave (n.) Look up leave at Dictionary.com
"permission," Old English leafe "leave, permission, license," dative and accusative of leaf "permission," from Proto-Germanic *lauba (cognates: Old Norse leyfi "permission," Old Saxon orlof, Old Frisian orlof, German Urlaub "leave of absence"), from PIE *leubh- "to care, desire, love, approve" (see love (n.)). Cognate with Old English lief "dear," the original idea being "approval resulting from pleasure." Compare love, believe. In military sense, it is attested from 1771.