Place oven rack in middle position and preheat oven to 450 degrees F. Line a baking sheet with parchment paper (or lightly spray) and set aside.
Toss together the chopped strawberries and 2 tablespoons flour, and set aside.
Place the remaining 2 cups of flour, sugar, baking powder and salt in the base of a food processor and pulse together until combined, about 2-3 times. Add the coconut oil in pinches, then pulse until mixture looks like course cornmeal, about 10-12 times.
Place the flour mixture in the base of a large bowl and add the flour-coated strawberries. Stir in the oat milk and 1 teaspoon lemon zest until a dough begins to form, about 30 seconds.
Turn the dough onto a lightly floured counter and form into a ball. Slice into 8 sections (1/2, then 1/2, then 1/2) and place onto the baking sheet, about 2 inches apart.
Bake for 13-15 minutes until golden brown. Let cool on a wire rack for 10 minutes.
Whisk together the remaining teaspoon lemon zest, juice, and powdered sugar until creamy, adding more sugar/lemon juice as needed. Then drizzle over the scones and let them harden, about 5 minutes. Eat!