Preheat the oven to 350° F. Grease the bottom of a 9x13 cake pan with margarine and dust with gluten free flour to coat it.
Combine the oil, applesauce, vanilla, milk, lemon juice, and sugar in a mixing bowl and mix well. Place a fine-meshed strainer over the mixing bowl and pour in the flour, baking powder, baking soda, and salt. Lightly tap the strainer until the dry ingredients have been sifted into the mixing bowl. Mix the dry ingredients into the wet ingredients. Beat for 30 seconds at medium speed.
In a separate bowl, melt the margarine and add the brown sugar and cinnamon. Mix well.
Pour half of the batter into the prepared pan and spread evenly (batter will be thick). Next, sprinkle half of the brown sugar and margarine mixture over the batter. Use a spoon to spread evenly over the batter. Add the remaining batter, spreading evenly, and top with the remaining brown sugar mixture.
Bake in a preheated oven for 25-30 minutes or until a toothpick inserted into the center of the cake comes out clean. Allow to cool for 10-15 minutes and then cut into squares.