Run the peach quarters through a juicer and pour the fresh peach juice into a large pitcher filled halfway with ice.
If you do not have a juicer, puree the peaches in a blender or food processor. Then strain through a fine mesh sieve into a large pitcher filled halfway with ice.
Add lemon juice, sugar, vodka and water to the large pitcher with peach juice.
Stir to combine until the sugar has dissolved.
Serve cold.