Hi Carol
Welcome to the forum! There is a regular Sunday walking group who do walks along the Lycian way...but they do stop in the early summer as it just gets too hot - if you do a search on the forum - you will find threads and organisers that you can send a message to. I know that the Wednesday strollers have hung up their boots for the summer..!!
Other than that - there are books marking the Lycian way but if you are anything like me - I would not want to venture off by myself - preferring to go with a walking group because the red markers are not always that easy to spot..!! I walk in trainers and adequate but obviously walking boots would be better but not worth the expense of excess luggage!
Enjoy Kalkan - you will have a brilliant time!