Wash the peach and slice it into thin pieces. In a saucepan, combine peach slices with sugar, water, and rosemary. Heat on medium until sugar dissolves, about 5 minutes.

Cover the pot and remove from heat, allowing it to steep for 10 minutes.

Strain the syrup through a fine-mesh sieve into a bowl. Press on solids to extract syrup and discard remnants.

Let syrup cool to room temperature for about 10-15 minutes.

Juice the lemons to yield 1 cup of juice. In a pitcher, combine cooled syrup and lemon juice, and 4 cups of filtered water, adjusting to taste.

Stir well until blended.

Fill glasses with ice and pour the lemonade over. Garnish with a sprig of rosemary or a slice of peach.