In a medium saucepan, over medium to low heat, soften the rhubarb and strawberries. Once they are soft, turn the heat off and press the fruit through a hand mill. Reserve the juices and discard the pulp and seeds.
In a medium saucepan, heat the sugar and water, until the sugar is dissolved. Remove from the heat and let cool slightly. Pour the mixture into a 1-gallon container, along with the lemon juice and fruit juices. Stir with a wooden spoon and add plenty of ice to fill the container. Add frozen strawberries for garnish and enjoy over ice.