Preheat oven to 350°F (180°C). Grease and flour two 9-inch cake pans with gluten-free flour or line with parchment paper.
Mix dry ingredients: In a bowl, whisk together the gluten-free flour, baking powder, salt, and lemon zest.
Cream butter and sugar: In a large mixing bowl, beat the butter, sugar, and oil until light and fluffy.
Add eggs and vanilla: Beat in eggs one at a time, then add vanilla extract.
Combine wet and dry: Alternately add the dry ingredients and milk to the butter mixture, beginning and ending with the dry ingredients. Mix until smooth.
Add lemon juice: Stir in the lemon juice and lemon zest for bright flavor.
Bake: Divide batter evenly between the prepared pans. Bake for 25-30 minutes or until a toothpick inserted in the center comes out clean.
Cool: Let cakes cool in pans for 10-15 minutes, then turn out onto wire racks to cool completely.
Make lemon syrup (optional): Combine sugar, lemon juice, water, and lemon peel in a saucepan. Bring to a boil, then simmer until sugar dissolves. Brush syrup over cooled cakes for extra moisture.
Prepare frosting: Beat butter until creamy. Gradually add powdered sugar, alternating with lemon juice and extracts, until smooth and spreadable. Add food coloring if desired.
Assemble cake: Place one cake layer on a plate. Spread a layer of frosting on top. Add the second cake layer and frost the top and sides evenly.
Store: Keep leftover cake in an airtight container at room temperature.