Place the chopped peaches in a blender or food processor. Blend on high speed until the peaches are completely pureed and smooth.
Pour the peach puree through a fine-mesh strainer into a large bowl, using a spoon or spatula to press and extract as much liquid as possible. Discard any solids left in the strainer.
Stir the cold water into the strained peach liquid until fully combined.
Add the sugar and lemon juice to the peach mixture, stirring until the sugar is completely dissolved and the mixture is well incorporated.
Taste and adjust sweetness or tartness by adding more sugar or lemon juice if desired.
Chill the peach nectar in the refrigerator for at least 1 hour before serving to enhance the flavor.