I use the modern name of the nearby village, the one you’ll take a dolmuş to for a visit (about once an hour from Fethiye, leaving there on the full hour, return is similar). However, the older name is Karmalyssos.

The Wikipedia has: “Kayaköy, anciently known as Lebessos and Lebessus (Ancient Greek: Λεβέσσος) and later as Livissi (Greek: Λειβίσσι) is a village 8 km south of Fethiye in southwestern Turkey. In ancient times it was a city of Lycia, Later, Anatolian Greeks lived there until approximately 1922. The ghost town, now preserved as a museum village, consists of hundreds of rundown but still mostly standing Greek-style houses and churches which cover a small mountainside and serve as a stopping place for tourists visiting Fethiye and nearby Ölüdeniz.
Livissi/ Kayaköy village. Its population in 1900 was about 2,000, almost all Greek Christians; however, it is now empty except for tour groups and roadside vendors selling handmade goods. However, there is a selection of houses which have been restored, and are currently occupied.“ Also “At the ending of the Greco-Turkish War (1919–1922), Kayaköy was already completely abandoned. The persecutions of Livissi inhabitants as well as Greeks of nearby Makri, were part of the wider campaign against all Ottoman Greeks and other Christians of the Empire. The persecutions in the area started in 1914 in Makri. In 1916, a letter in Greek addressing to sir Alfred Biliotti, the Consul General of Great Britain at Rhodes, explained the murders and persecution of Livissi and Macri Greeks who asked him for intervention. Unfortunately, the letter was intercepted at Livissi by Turkish authorities. Later that same year, many families of Levissi were deported and driven on foot to Denizli, around 220 km away. There, they suffered various extreme atrocities and tortures, facing even death.
Two more exile phases followed in 1917 and 1918. In 1917, families were sent in villages near Denizli, such as Acıpayam, through forced march of fifteen days, consisting mainly of the elderly, women and children, who had remained in the area. During that death march, the roads were strewn with bodies of dead children and the elderly who succumbed to hunger and fatigue. The exiles of the next year were no less harsh. In September 1922, the few remaining Greeks of Livissi and Makri abandoned their homes and embarked on ships to Greece. Some of them founded Nea Makri (New Makri) in Attica. Many of the abandoned buildings were damaged in the 1957 Fethiye earthquake. “

I went here three times in 2016, two times by dolmuş from Fethiye, one time walking from there. On the first occasion I visited the nearby village, on the thikrd I intended to take some pictures from the plain with the village and Kayaköy in the distance, but persistent attacks by a bee forced me to run for cover and I let it be. On the first visit, after a short while, clouds and mist made for some fine effects, but it got cold and I was afraid it might rain. On that occasion I went for the eastern side of the hill. On the second visit I did the rest, including a chapel on a high hill to the west. I met several walkers, who seemed to be on (well indicated) tracks from for instance Ölüdeniz.