Preheat oven to 350 degrees F and lightly grease an 8x8-inch baking dish; set aside.
Combine the flour, oats, salt and baking soda in a medium sized mixing bowl. Using a wooden spoon, stir in the sugars until thoroughly combined. Add the vanilla and melted butter and mix until the dry ingredients are just moistened. Gently press half of the mixture into the bottom of the prepared pan.
Bake for 15 minutes then remove from the oven and set aside, leaving the oven on at 350 degrees.
For the lemon filling:
Whisk together the condensed milk, lemon zest and juice, egg yolks and vanilla in a medium bowl until smooth. Pour into the baking pan over the baked crust. Spread evenly. Crumble the remaining oatmeal crust evenly over top.
Bake at 350 for 25 minutes, until light golden.
Remove and let set to cool at room temperature (about 1 hour). Refrigerate for 1 more hour and cut into squares once cooled, or serve warm with ice cream. Store covered in the fridge.
Serve cold, room temperature, or warm with ice cream.