In a small bowl, sprinkle gelatin over 1/4 cup cold water. Set aside to soften, about 5 minutes.
Meanwhile, in a small saucepan, combine sugar, salt, and 1/4 cup water. Heat over high, stirring occasionally, just until sugar is dissolved, 2 to 3 minutes; remove from heat. Stir in gelatin mixture until dissolved; set aside.
In a blender, combine lemon juice and half the watermelon chunks; puree. Add remaining watermelon chunks; puree. Pour puree through a fine-mesh sieve into a large bowl or glass measuring cup, and discard solids. (You will need 3 cups of puree; reserve any extra for another use.)
Stir gelatin mixture into puree; skim off and discard any foam on the surface. Divide mixture among 6 serving cups. Cover and refrigerate until set, at least 3 hours and up to 3 days. Serve gelatins, garnished with diced watermelon.