Peel and pit the peach, then slice it into bite-sized chunks or thin wedges, as you prefer. Cover it with sugar and let it macerate at least one hour.
Meanwhile, place the rest of the peaches in a blender along with the sugar, water and lemon juice. Blend until smooth.
Transfer the peach purée to an ice cream maker and freeze until the purée reaches a soft-serve consistency. Just before it's ready, add in the macerated peach and continue until the peach bits have chilled. Take care that they don't actually freeze.
Serve right away