In a medium saucepan, bring 2 cups of water to a boil together with the sugar and one whole lemon peel until the sugar is completely dissolved. Then transfer the mixture into a large bowl and let it cool to room temperature.
Juice the 6 lemons and strain the pulp. Then add the juice to the sugar syrup.
In another mixing bowl, use an electric hand mixer or electric whisk to whip the egg white for 5 to 7 minutes or until stiff peaks form.
Gently fold the whipped egg white into the lemon mixture with a rubber spatula. It should be foamy. Then pour the mixture into a metal baking pan or loaf pan and place it in the freezer.
After 1 hour, mix the mixture with a hand whisk or an electric whisk to create a fine texture with no ice crystals. Then put the sorbet back in the freezer and repeat this process 2 to 3 more times every hour.
When the lemon sorbet is ready, it should have a solid but creamy, frothy consistency that doesn't have any chunks of ice.
Serve the sorbet immediately or store it in the freezer in an airtight container for up to 1 month.