Don't be tempted to use juice from a bottle -- with so few ingredients, every one really counts.
In a small saucepan, heat 2/3 cup sugar and 1/4 cup water over medium-high, stirring occasionally, until sugar is dissolved, 3 minutes. Stir in lemon juice. Transfer to a large bowl and let cool completely, about 30 minutes.
In a large bowl, using a mixer, whisk egg whites on high until foamy, 1 to 2 minutes. Reduce speed to medium and gradually add remaining 1/3 cup sugar. Increase speed to high and whisk until stiff, glossy peaks form, 2 to 5 minutes. With a rubber spatula, gently fold egg white mixture into lemon juice mixture.
Pour into a 9-inch square baking dish. Freeze until just set, about 2 hours. Mixture will have separated into 2 layers; scrape with a fork to recombine. Freeze until firm, 4 hours more (or, covered, up to 3 days). Scoop into dishes and serve immediately.
If you're concerned about consuming raw eggs, use pasteurized egg whites instead.