1. Dissolve the sugar in the hot water over low heat. Bring to a boil. Lower the heat, and simmer for approximately 5 minutes, or until the temperature on a candy thermometer reads 216Â°F.
2. Cool, stir in the lime juice, and chill thoroughly.
3. Freeze in a mechanical freezer (I use the Waring's Ice Cream Parlor) for 20 minutes, or until the mixture resembles melted snowâ€”slushlike.
4. Beat the egg white and fold it and the food coloring into the lime slush. Continue freezing for 20 minutes, or longer, if needed.