Juice the Lemons: Roll the fresh lemons on the counter to soften them, slice, and juice until you yield one full cup. Discard any seeds.
Load the Blender: Add the frozen peaches, lemon juice, sugar, and cold water to the pitcher of a blender.
Blend the Base: Pulse a few times to break up the frozen fruit, then blend on medium-high for 45 seconds until smooth.
Add Ice: Drop the ice cubes into the blender and run for an additional 30 seconds until a thick, slushy texture is formed.
Serve: Pour immediately into chilled glasses, garnish with a lemon wheel and fresh mint, and enjoy.