Preheat oven to 350 degrees F. Line baking sheets with parchment or silicone baking mats, if desired, and set aside.
Using an electric mixer if possible, cream together the butter and brown sugar on high speed until the mixture is light and fluffy. Add egg and vanilla, scrape down the sides of the bowl, and mix well to combine.
Sprinkle the flour, oats, cinnamon, baking soda, cloves, and salt over the dough. Mix on low speed until mostly even.
Sprinkle lemon juice over chopped apples and toss gently. Add apples to the cookie dough and stir gently to combine. Scoop dough into rounds of about 2 tablespoons each, place slightly apart on the prepared baking sheets, and press down gently to flatten a bit.
Bake for 12-14 minutes, until the tops are set and the edges are lightly golden. Cool for 5-10 minutes on the baking sheets, then transfer to a wire rack to cool completely.
To make the maple glaze, combine powdered sugar, milk, and maple syrup in a small bowl. Whisk or stir well until smooth. Add more syrup or powdered sugar to adjust the consistency as desired. Use a spoon to drizzle glaze over the cookies, and set aside, without stacking, until the glaze sets.