Combine eggs, water, milk, and oil in a mixing bowl and whisk until the mixture becomes smooth. Add the cake mix powder and stir just enough to combine. It's okay if there are some lumps, but be careful not to overmix the batter.
Grease and flour a rectangular cake pan measuring 9x13 inches and pour about three-quarters of the batter into the pan. In a separate mixing bowl, coat the apples with brown sugar, cinnamon, nutmeg, and lemon juice until the apples are fully coated.
Spread the apple mixture over the cake batter in the pan, then pour the remaining cake batter on top. The apples won't be fully covered by the batter, but that's fine. To make the topping, mix flour, coconut, brown sugar, and butter with a fork until the mixture becomes crumbly. Sprinkle this topping over the apples and cake batter.
Bake the cake at 350 degrees for approximately 45 minutes, or until an inserted toothpick in the center comes out clean. Allow the cake to cool completely before making the sugar glaze. Combine powdered sugar, milk, and vanilla extract in a bowl and whisk until the mixture is smooth and perfect for drizzling. Add more milk if you want the drizzle to be thinner, or more powdered sugar if you want it thicker.Drizzle the glaze over the cake and enjoy!