Hi and welcome to
Symi ChatI'm afraid there are no trips to Loryma despite its proximity to Symi. I doubt there would be enough interest to make an organised trip viable. Also, I believe (though I'm no expert) that visits to Turkey have to be to ports with the necessary police and immigration staff to process visitors' papers. I think that means Datca or Marmaris, both a long way from Loryma. There was talk a few years ago of trips to Selimiye but nothing came of that.
Sorry