In a small saucepan over medium heat, cook honey, water, and thyme, stirring constantly and bruising thyme leaves as you stir, until honey has dissolved, about 2 minutes. Let cool to room temperature, then discard thyme.

Make Ahead: Honey syrup can be made 2 weeks ahead. Transfer to an airtight container and chill.

In a cocktail shaker, combine gin, lemon juice, and 3/4 oz. honey syrup. Fill shaker with ice and vigorously shake until outside of shaker is very cold, about 20 seconds.

Strain into a coupe. Garnish with lemon and thyme.