Add sliced peaches, sugar, and water to a saucepan.
Place on medium heat and bring to a gentle simmer.
Stir occasionally until sugar dissolves completely.
Simmer for 12–15 minutes until peaches are very soft and fragrant.
Remove from heat and allow syrup to cool slightly.
Strain mixture through a fine sieve into a bowl.
Press lightly while straining to extract flavor without forcing excess pulp through.
Stir in fresh lemon juice into the strained syrup.
Fill serving glasses with ice cubes if desired.
Pour peach syrup. Add syrup to taste (about ¼ to ⅓ of the glass) before topping with sparkling water.
Top with chilled sparkling water.
Stir gently and garnish with fresh peach slices.