Combine 1 quart water and sugar in a Dutch oven. Bring to a boil; reduce heat, and simmer 20 minutes or until slightly thickened. Soften gelatin in 1/2 cup cold water. Add softened gelatin to syrup mixture; stir until gelatin completely dissolves. Cool.
Combine gelatin mixture, apricots, orange juice, and lemon juice; stir well.
Beat egg whites (at room temperature) until stiff peaks form. Fold into apricot mixture. Pour into freezer can of a 1-gallon hand-turned or electric freezer. Freeze according to manufacturer's instructions. Let ripen 1 hour before serving.