Heat oven to 350° F. Lightly grease a 13 x 9 x2-inch glass baking dish.
Combine the sweetened condensed milk, lemon juice, and lemon zest in a medium bowl; set aside.
Measure out ¼ cup white baking chips and place in a separate bowl. Measure out 1/3 cup white baking chips in another separate bowl. The remaining chips add to the lemon filling mixture. Stir to combine. Set aside.
In the bowl of your stand mixer, beat the brown sugar and butter at medium speed until well blended.
In a large bowl, stir together flour, oats, pecans, baking powder, and salt. Add to butter mixture in the mixing bowl. Blend well. Set aside 1 and 2/3 cups of oats mixture for the crumb topping.
Add the egg to the remaining oat mixture in the mixing bowl. Mix until well combined. The mixture will be slightly crumbly. Press evenly into the bottom of the prepared pan.
Gently spoon lemon mixture on top, spreading evenly. Add the reserved 1/3 cup white chips to the reserved oat crumb streusel mixture. Sprinkle over lemon layer, pressing down lightly.
Bake 20–25 minutes or until lightly browned. Cool in pan on a wire rack. Place the remaining ¼ cup white chips in a microwave-safe bowl with shortening. Microwave at MEDIUM (50%) power for 30 seconds or until the chips are melted, and the mixture is smooth when stirred. Drizzle over the baked bars. Allow drizzle to set; cut into bars.