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type of citrus fruit, c.1400, lymon, from Old French limon "citrus fruit" (12c.), via Provençal or Italian from Arabic laimun, from Persian limu(n), generic terms for citrus fruits (cf. lime (n.2)); cognate with Sanskrit nimbu "the lime." Slang meaning "a Quaalude" is 1960s, from Lemmon, name of a pharmaceutical company that once manufactured the drug.
"worthless thing," 1909, American English slang; from lemon (n.1), perhaps via criminal slang sense of "a person who is a loser, a simpleton," which is perhaps from the notion of someone a sharper can "suck the juice out of." A pool hall hustle was called a lemon game (1908); while to hand someone a lemon was British slang (1906) for "to pass off a sub-standard article as a good one." Or it simply may be a metaphor for something which leaves a bad taste in one's mouth.
[1960s+ Narcotics; Lemmon is the name of a pharmaceutical company that once manufactured the drug]