In a small saucepan over medium heat, combine sugar with 1 cup water. Stir gently until mixture comes to a simmer and sugar dissolves. Add lavender and rosemary, if using; simmer an additional 5 minutes.
Remove from heat and steep for at least 30 minutes. Strain into a jar, cover, and chill until ready to use.
Lavender Lemonade:
Combine 1 cup fresh lemon juice, 1 cup lavender simple syrup, and 2 cups cold water. Stir well. Add ice and more lavender simple syrup, if desired.
Lavender Lemon Drop Martini:
Moisten rim of glass with lemon juice. Dip in sugar. In a cocktail shaker, combine 1 cup ice, 1 1/2 ounces vodka, 1 ounce lavender simple syrup, and 1 tablespoon lemon juice. Shake until cold. Strain into prepared glass and garnish with a strip of lemon zest and a sprig of lavender.