Preheat the oven to 350 degrees and line a baking sheet with parchment paper.
In a small bowl, mix the egg replacer with water according to the instructions on the package. Set aside.
In a medium sized mixing bowl, add the all-purpose flour, oats, cinnamon, baking soda and salt. Whisk until combined.
Using either a stand mixer or a hand held mixer, cream together the butter and the brown sugar until combined. Add the egg replacer and pure vanilla extract and mix.
Toss the diced apples with lemon juice in bowl. Add flour mixture to egg and vanilla mixture and mix until combined, then stir in the apples.
Using a medium cookie scoop, scoop approximately 2 tbsp of dough and drop it onto the lined cookie sheet. Flatten them slightly.
Cook for 14-15 minutes or until the edges are slightly browned. Let the cookies cool on the baking sheet for 10 minutes, then transfer to a wire cooling rack to cool completely.
Make the salted caramel according to the directions in this post. Drizzle the caramel onto the cooled cookies using either a fork or spoon.