Linchpin is the usual spelling of the noun referring to (1) a central cohesive element, or (2) a locking pin inserted in the end of a shaft to prevent a wheel from slipping off. The word derives from the Middle English linspin, which in turn derives from Old English elements. Although lynchpin is a somewhat common variant, its first syllable’s association with the unrelated verb lynch perhaps counts against it.
Examples
Both spellings appear in all varieties of English. In British and Canadian English, linchpin appears about twice as often as lynchpin, but both appear in some major news publications—for example:
The lynchpin city of the regime, Tripoli, is yet to fall, but some of its districts have. [Telegraph]
The linchpin of the e-governance system is a website through which residents will be able to pay their bills. [Guardian]
But positioning Mr. Harrison at the helm of CP is the lynchpin of a turnaround plan led by Mr. Ackman. [National Post]
No one gets the sequential oddity of Chandler succeeding Curry as the Knicks’ high-priced linchpin centre better than Chandler. [Globe and Mail]
Lynchpin appears much less frequently in American English, perhaps because the verb lynch is more present in Americans’ minds. Linchpin is standard in contexts like these:
Kelly was one of the four players the Red Sox traded to San Diego for Adrian Gonzalez and was the linchpin of the deal. [Boston Globe]
Environmental groups are reassessing their willingness to see nuclear power as a linchpin of any future climate change legislation. [New York Times]
To a disparate clan like the Dollys, meth was the one linchpin. [Los Angeles Times]