The derivation of this "lock" is not 100% clear.

OED:

"The... Lock Hospital in Southwark ... was probably so called on account of being specially isolated or quarantined, and some early sources discuss the security of the hospital and the need for inmates to be kept out of the city. An alternative suggestion that the name is derived from Middle French 'loque' rag ( < Dutch locke lock n.1), with reference to the rags with which the sores of lepers were dressed, seems less likely and cannot be substantiated."

"Seems less likely" doesn't mean "wrong," but "cannot be substantiated" means there's no contemporaneous evidence for it and so no reason to prefer it.

Conceivably (which means no more than "just a suggestion"), the application of "lock" owes something to the similarity of the French (or even Dutch)and English words, but precisely which "came first" would currently be unknowable - and could not have been generally known at the time.