Combine 1 cup of lychees, lemon juice, sugar, salt, and Thai chili in a blender. Blend on high speed until smooth, about 1 minute.
Strain through a fine mesh strainer into pitcher. Discard solids.
Add cold water and whisk to combine.
Chop remaining lychee flesh into ¼-inch pieces and add to pitcher.
Add ice.
Serve in ice-filled glasses garnished with additional whole chilis if desired.
