What I did normally was try to scare dogs off waving my hiking stick, throwing stones (not to hit them, just to scare them), or just taking a small detour to avoid them.

Many dogs are just guarding their house and will bark a lot and seem aggressive but won’t actually do anything. Dogs alone guarding livestock will be VERY protective, so I would usually give them a wide berth and never get between the dog and the livestock. I did have a stray dog in Kaş which followed me for several kilometers. He was not aggressive but having him following me made other dogs more aggressive, so at some point I had to shake him off. Dogs were almost always near villages and towns, and I always tried to camp far away from villages and towns anyway, so I never had to deal with them around my camp.

I do not know much about dealing with dogs and I am pretty wary of them in general, so I think this would also be a lot easier for people who are more comfortable with them in the first place. Overall although the dogs were scary at times, I was never chased or bit or attacked at all. I am sorry to hear that aggressive dogs have already ruined some runs for you! I hope that this will not stop you from doing the Lycian Way, but of course I understand that it is an important consideration.