Stir strawberries, 1/4 cup sugar, and lemon juice in a small nonreactive pan; bring to a simmer over medium heat. Cook, stirring often, until softened, about 3 minutes. Remove strawberries; place in a bowl and let cool. Set aside pan with strawberry liquid.
Meanwhile, in another small pan over medium-low heat, combine rhubarb, remaining 1/3 cup sugar, and the water. Simmer gently, stirring often, until sugar is dissolved and rhubarb is almost tender, about 6 minutes. Using a slotted spoon, transfer rhubarb to bowl with strawberries. Add strawberry liquid to pan.
Raise heat to medium and simmer until thickened and reduced to 1/2 cup, about 10 minutes. Let cool. Stir into strawberry-rhubarb mixture.
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