Preheat the oven to 350 degrees F. Grease a 9x13 baking pan with nonstick baking spray.
In a large mixing bowl, add the 1 cup butter, 2 tablespoons vegetable oil, 1 1/4 cups granulated sugar, 16 ounces almond paste, and 2 tablespoons lemon zest. Using a hand mixer on medium speed, beat until creamed and the almond paste is well blended. This could take 2 to 3 minutes.
Add the 3 large eggs, 1 teaspoon almond extract, and 1/2 teaspoon lemon paste. Beat until the eggs are worked into the batter. Scrape down the sides of the bowl.
In a liquid measuring cup, add the 1/2 cup fresh lemon juice and 3/4 cup buttermilk.
In a medium bowl, add the 2 1/2 cups all-purpose flour, 1 teaspoon baking powder, 1/2 teaspoon baking soda, and 1/2 teaspoon salt. Whisk until combined.
Start alternating adding the the dry ingredients and buttermilk mixture starting and finishing with the dry ingredients. Scrape down the sides of the bowl after each addition.
Scoop the cake batter into the prepared baking pan and spread out evenly to the sides of the pan.
Place in the preheated oven and bake for 45 to 50 minutes until a toothpick inserted in the middle of the cake comes out clean or with moist crumbs. If testing by gently pushing on the top of the cake, it won’t bounce back right away when it’s done.
Remove from the oven and whip up the glaze to pour on it while the cake is still warm.
Add the sliced almonds on a rimmed baking pan and spread out into one even layer.
Place in the 350 degree F oven for 5 minutes until slightly golden and fragrant.
Glaze
In a small bowl, add the 1/4 cup fresh lemon juice and 2 cups powdered sugar. Whisk until smooth.
Pour almost all of the glaze on the hot cake and spread out using an angled spatula to coat the entire cake.
Sprinkle the toasted 1/4 - 1/2 cup sliced almonds on top of the glaze.
Drizzle the remaining glaze on top of the sliced almonds.
Let cool completely before serving.
Store in an airtight container at room temperature.
Notes
Storage: You can store your cake in an airtight container on the counter for 3-4 days. Now, you can extend the shelf like to 4-5 days if you store the cake in the fridge.Freezing: You can also freeze slices of the cake, or the whole cake in a freezer-friendly container or bag. Freeze for 2-3 months. Then thaw on the counter or in the fridge overnight.