In a large saucepan, combine the rhubarb and 1/2 cup sugar. Bring to boiling stirring constantly. Reduce heat, simmer 6-8 minutes, or until sauce forms. Pour into bowl, refrigerate about 2 hours, or until cold.
In a food processor, combine strawberries, remaining 1/2 cup sugar and lemon juice. Process strawberries until finely chopped but still frozen. With motor running pour in cream. Process until creamy, but still frozen, scrapping sides frequently. Spoon ice cream into large bowl. Fold in rhubarb sauce just until combined. Freeze 2 hours or overnight, or until firm. If frozen overnight let stand for 15 minutes.