Pour the lemon juice through a fine mesh strainer into a small pot to make sure there are no stray seeds or pulp. Add the sugar, basil and rum to the pot as well and heat it over medium heat. Let the mixture warm up just enough to dissolve the sugar while you stir it for about 30 seconds to a minute. Take it off of the heat and pour it into an 8 x 8 baking pan and get it into the freezer on a level shelf. Let it freeze for an hour, then take it out and fluff up any crystals with a fork. Put it back in and repeat each hour until it has frozen for 4 hours total. It will end up looking like fluffy, icy snow. Serve immediately with whipped cream on top and garnished of chopped basil and lemon zest!