This street in Madison Park — one I remember from childhood, as I was interested in maps and streets even then, and this one wasn’t part of the regular grid — is essentially a driveway for three houses. Only 100 feet long, it hangs off E Lee Street between 42nd Avenue E and the Lake Washington shoreline like an afterthought, which indeed it was, appearing neither on the 1875 plat of John J. McGilvra’s 2nd Addition to the City of Seattle nor the 1908 Board of State Land Commissioners’ Map of Lake Washington Harbor. The first reference to it in The Seattle Times is in 1925. I couldn’t find an ordinance establishing it, but I did find Ordinance 63622, passed in 1933:
An ordinance accepting deeds from Hubert W. Youngs and Maude E. Youngs, husband and wife, Harry Richmond, William G. Knox, and Bessie S. Woodworth, for an easement for sewer over and across a portion of J. J. McGilvra’s 2nd Addition and Lake Washington Shore Lands.
Since Knox Place is very close to where the two plats meet, I figure it’s a good bet that William G. Knox has something to do with Knox Place. FamilySearch says a William Gifford Knox (1884–1964) lived in Seattle for a time, and even had a scan of his draft registration card for World War I, from September 12, 1918. He appears to have been a salesman for the Dennison Manufacturing Company downtown, and his address is given as 1836 Laurel Shade Avenue. That street is now 43rd Avenue E, putting his residence just a few blocks north of Knox Place E. So, although I don’t have the whole story, I think we now know who Knox Place is named for.