Cut ribs of rhubarb in half lengthwise and slice into ¼-inch pieces; place into a bowl. Add cubed strawberries and 2 tablespoons sugar. Toss to combine, cover, and let fruit macerate in the refrigerator for 1 to 2 hours.

Combine flour, baking powder, baking soda, and salt in a mixing bowl; whisk to combine.

Drain fruit in a strainer set over a bowl. Reserve the syrupy juices that pass through.

Grate frozen butter into the flour mixture, while stirring with a fork several times to coat butter pieces with flour. Add ¼ cup sugar, and drained fruit, mixing with a fork until fruit is coated with flour.

Add 2 tablespoons of the reserved fruit juices, and pour in buttermilk. Mix with a fork just until the dry ingredients are incorporated into the dough. If the mixture is too dry to come together, add a little more buttermilk. If it seems too wet, and sticky, add a little more flour.

Preheat the oven to 450 degrees F (230 degrees C). Line a baking sheet with a silpat mat.

Scoop or spoon equal portions of dough onto the prepared baking sheet. Whisk together egg and water in a small bowl. Brush biscuits with egg wash, and sprinkle with sugar.

Bake in the preheated oven for about 25 minutes. Transfer to a wire rack and let cool completely.

Mix powdered sugar, lemon zest, and lemon juice together in a small bowl for the lemon icing. Fill icing into a piping bag or a plastic bag with the tip cut off and drizzle icing over cooled biscuits.