The story
In reference to Lindy's delicatessen in New York, where comedians would meet to discuss showbusiness. This was discussed in "Lindy's Law", a 1964 article by Albert Goldman in The New Republic. Goldman described a folkloric belief that the amount of material comedians have is constant, and therefore the frequency of output predicts how long their series will last.
Etymology from Wiktionary, CC BY-SA 4.0.