Add 1 cup water and 3/4 cup sugar to a small saucepan. Warm over medium heat, stirring until the sugar dissolves.
Remove the saucepan from the heat. Stir in the culinary lavender, cover, and steep for 8 minutes.
Strain the lavender syrup through a fine mesh strainer. Discard the lavender buds and let the syrup cool.
Add sliced peaches and 1/2 cup cold water to a blender. Blend until smooth.
Strain the peach puree for a smoother Lavender Peach Lemonade, or leave it pulpy for a more rustic texture.
In a large pitcher, stir together the peach puree, fresh lemon juice, cooled lavender syrup, and 3 cups cold water.
Taste and adjust. Add more cold water for a lighter drink, more lemon juice for tang, or a little extra sugar if needed.
Chill for at least 30 minutes.
Serve over ice with lemon slices, peach wedges, and a small lavender sprig.