For the honey syrup: Whisk together the honey and water in a small saucepan over medium heat. Bring to a simmer and stir until dissolved, about 1 minute. Cool and store in an airtight container for up to 2 weeks.
For the martinis: Stir together the lemon juice, vodka or gin, 3/4 cup honey syrup and 1 1/2 cups water in a carafe or pitcher. Wrap and refrigerate until chilled, 3 to 4 hours. When ready to serve, pour into chilled martini glasses and garnish with lemon wheels.
To make 1 serving to serve immediately, add 2 cups ice to a cocktail shaker, and then pour in 1 1/2 ounces vodka or gin, 1 1/2 tablespoons honey syrup and 1 1/2 tablespoons lemon juice. Shake, and then strain into a chilled martini glass. Garnish with a lemon wheel.