Combine peaches, lemon juice, sugar, and salt in a blender. Blend on high speed until smooth, about 1 minute.
Meanwhile, place thyme in bottom of pitcher and lightly muddle with wooden spoon.
Strain peach puree through a fine mesh strainer into pitcher. Discard solids.
Add cold water and whisk to combine.
Add ice.
Serve in ice-filled glasses garnished with peach slices and thyme leaves.
