I'm flying back from DLM next week. According to MMB there is no lounge at Dalaman, but according to the OW Lounge Finder the airport's CIP Lounge is for use by Club Europe and Sapphire/Emerald OW members travelling on BA.
I know the lounge is open, so it'll be interesting to see what is said at checkin. My LoungeKey pass gets me access in case BA don't.