Add peaches to a blender; blend until smooth. Measure out 1 1/2 cups peach puree into a bowl. Immediately stir in lemon juice and refrigerate.
Combine water and sugar in a small saucepan and bring to a boil. Stir until sugar is dissolved, about 1 minute. Remove from stove and cool to room temperature. Refrigerate simple syrup until chilled, about 1 hour.
Pour chilled peach puree and simple syrup into an ice cream maker and freeze according to manufacturer’s instructions, about 20 minutes. Transfer to an airtight container and freeze until firm, about 4 hours.