Preheat the oven to 425 degrees F (220 degrees C).
Line a baking sheet with parchment paper.
Whisk together flour, baking powder, baking soda, 1/3 cup white sugar, and salt in a mixing bowl.
Cut in cold butter with a knife or pastry blender until the mixture resembles coarse crumbs. (If desired, place flour mixture into the work bowl of a food processor with the butter; pulse several times to cut butter into the flour mixture. Transfer mixture to a mixing bowl, and proceed.)
Stir in buttermilk until the flour mixture is moistened.
Drop 1/3-cup scoops of the dough 2 inches apart onto the prepared baking sheet.
Brush biscuits with heavy cream and sprinkle generously with turbinado sugar.
Bake in the preheated oven until golden brown, 15 to 20 minutes.
Mix together the sliced strawberries, 1/4 cup white sugar, and lemon juice in a large bowl. Allow berries to rest until juices develop, about 30 minutes.
Serve the strawberries with juice over the biscuits.