lean (v.) Look up lean at Dictionary.com
c.1200, from Old English hleonian "to bend, recline, lie down, rest," from Proto-Germanic *khlinen (cognates: Old Saxon hlinon, Old Frisian lena, Middle Dutch lenen, Dutch leunen, Old High German hlinen, German lehnen "to lean"), from PIE root *klei- "to lean, to incline" (cognates: Sanskrit srayati "leans," sritah "leaning;" Old Persian cay "to lean;" Lithuanian slyti "to slope," slieti "to lean;" Latin clinare "to lean, bend," clivus "declivity," inclinare "cause to bend," declinare "bend down, turn aside;" Greek klinein "to cause to slope, slant, incline;" Old Irish cloin "crooked, wrong;" Middle Irish cle, Welsh cledd "left," literally "slanting;" Welsh go-gledd "north," literally "left" -- for similar sense evolution, see Yemen, Benjamin, southpaw).

Meaning "to incline the body against something for support" is mid-13c. Figurative sense of "to trust for support" is from early 13c. Sense of "to lean toward mentally, to favor" is from late 14c. Related: Leaned; leaning. Colloquial lean on "put pressure on" (someone) is first recorded 1960.
lean (adj.) Look up lean at Dictionary.com
"thin, spare, with little flesh or fat," c.1200, from Old English hlæne "lean, thin," possibly from hlænan "cause to lean or bend," from Proto-Germanic *khlainijan, which would connect it to Old English hleonian (see lean (v.)). But perhaps rather, according to OED, from a PIE *qloinio- (with cognates in Lithuanian klynas "scrap, fragment," Lettish kleins "feeble"). Extended and figurative senses from early 14c. The noun meaning "lean animals or persons" is from c.1200, from the adjective.
lean (n.) Look up lean at Dictionary.com
"action or state of leaning," 1776, from lean (v.).