Stir wine, sugar, lemon thyme, and 1/4 cup water in a saucepan. Bring to a simmer over medium-high heat. Reduce heat to medium-low; simmer 20 minutes.
Pour syrup through a fine sieve into a bowl; discard lemon thyme. Let cool slightly, about 5 minutes, before serving. Syrup can be refrigerated in an airtight container up to 1 week; reheat over medium-low heat before serving.