lean (n.2) Look up lean at Dictionary.com
c. 1200, "lean animals or persons," from lean (adj.). Meaning "lean part of anything, muscle without fat, lean meat" is mid-15c.
lean (n.1) Look up lean at Dictionary.com
"action or state of leaning, deviation from a vertical position," 1776, from lean (v.).
lean (v.) Look up lean at Dictionary.com
c. 1200, from Old English hlinian "to recline, lie down, rest; band or incline" (Mercian hleonian, Northumbrian hlionian), from Proto-Germanic *khlinen (source also of 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" (source also of 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").

Transitive sense "cause to lean or rest" is from 14c. 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 (Skeat) 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. In business jargon, paired with mean (adj.) from 1970s to suggest aggressiveness as if from hunger.