There was a cold limerick one time
whose rick was cut off from its lime.
While not quite a Lime Ricky,
its flavor was tricky
and sacrificed taste to the rhyme.
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To most New Yorkers, it means a cherry-tinged treat. To many New Englanders, it's a fizzy raspberry soda. For the purist, it's all about the lime—and only the lime. One thing's certain: The lime rickey is the soda fountain's comeback kid.
A refreshing mix of lime juice, fruit or sugar syrup, and seltzer, the lime rickey owes its origin to its alcoholic forefather. Sometimes referred to simply as "a rickey" or "gin rickey," the drink was famously concocted at Shoomaker's bar in Washington D.C. in the 1880s.
http://www.seriouseats.com/2015/04/lime-rickey-soda-fountain-history.html