Soften gelatin in cold water. Combine boiling water and sugar in a heavy saucepan; boil 5 minutes. Remove from heat; add lime juice, salt, and softened gelatin, stirring until gelatin dissolves. Add green food coloring, if desired. Let cool.
Beat egg white (at room temperature) until stiff but not dry. Fold into gelatin mixture. Spoon into a 2-cup metal ice tray (with divider removed). Freeze until mixture becomes slushy. Remove from freezer; stir well.
Return to freezer; freeze until mixture reaches the consistency of a sherbet. Scoop into sherbet dishes, and serve immediately.