Just saw this posting.
I GPSed some of the Lycian Way in 2004 while on a work party led by Kate. We however mountain biked some of the trail and also rode around parts of the trail that were too difficult for mountain bikes. And we also drove in a vehicle past parts of the trail that didn't need work.
If this is useful, I'll try to wade through my other track information and post it. This trip was my first use of a GPSr, and the data is almost three years old.
These are more or less in order from from the western end heading south (east). Clicking on the links may result in the data loading in the page. Just save the page. If ".txt" is added to the name of the file, remove the ".txt" and then double click on the .kmz file to see the route in Google Earth
Lycian Way A
Lycian Way B
Lycian Way C
Lycian Way D
Lycian Way E
Lycian Side Trip
I edited this several hours after the initial posting to add more pieces. I still a bit more of the route coming into Kas.