The pedestrian dirt pathway around Green Lake, most of it near the shoreline, was measured via surveyors rod & chain in 1946 for a collegiate cross country race - and again in 1952 for Pacific Northwest AAU cross-country championship race. Both measurements, witnessed by me, were 2.82 miles.
Several national championship footraces used the dirt pathway until it was paved in 1967. The longest run there was a marathon -- 26 miles 385 yards.
The place that pathway is furthest from the shore, even now, is behind the West Green Lake "bath-house" which has been converted to a community theater.
A different (relatively narrow) path around the lake is just inside the paved road used by automobiles. Perhaps I can push my surveyor's wheel around that path when I visit Seattle in August 2014.