Robert Hendrickson, QPB Encyclopedia of Word and Phrase Origins
, 2nd edition (New York: Facts on File, 2004), p. 284, gives the following explanation of the origin of the word expedite
An old story that no one has been able to prove or disprove holds that the Latin word expedire, the ancestor of expedite, derives from the name of St. Expeditus, a soldier in the Roman Army before being martyred at Melitene, Armenia, in the fourth century. St. Expeditus, it seems, was the advocate of urgent causes. The O.E.D. merely says that the Latin word expedire means "to free a person's feet (ped) from fetters, to help forward, to dispatch, send off."
It's quite easy to prove that Latin expedire
does not derive from the name of a fourth century A.D. St. Expeditus. The word occurs in the earliest Latin writers, for example in numerous passages of Plautus, a writer who died in the second century B.C. I don't know where Hendrickson got his old story, but it's arrant nonsense.