Measure your sugar into a bowl and zest the lemon into the bowl of a stand mixer. Rub the zest into the sugar, cover and set aside.
Preheat the oven to 350°F (177°C/gas mark 4).
Cut out parchment rounds that will fit flat into the bottom of the cake pans. Spray the pans with baking spray and line the bottom of them with the parchment. Spray the parchment once more.
Make the batter
Add the flour, baking powder, baking soda and salt to the sugar mixture. Using the paddle attachment of the stand mixer, mix well until combined.
Add the softened butter and mix well, until everything is fully combined.
Add in the oil and mix well.
Add in the eggs, buttermilk, lemon juice and lemon extract if you are using it.
Making sure to scrape down the bowl occasionally, mix until everything is combined. Once it is fully combined, beat for another 20-30 seconds to strengthen the batter.
Bake
Add the batter to the two pans, using your kitchen scale to help you get about the same amount of batter in each pan.
If you are using cake strips, saturate them with water and wrap them around the sides of the pans.
Bake for about 30 minutes, until the tops of the cakes spring back and the internal temperature is 205°F (96°C).
Allow the cakes to cool for about 10 minutes in the pan. Then flip them out onto a cooling rack and let cool to room temperature.
Flavor the buttercream
Mix together the lemon juice and citric acid until the citric acid is fully dissolved.
Add the juice and lemon extract (and food coloring, if you like) to the buttercream and beat until all is combined and the buttercream is fluffy.
Construct the cake
Cut the cake layers in half using a large serrated knife or a cake leveler.
Place the bottom layer of cake onto a cake board, securing it with a dollop of buttercream underneath. Place the cake board on a turntable. Add a layer of buttercream and then place the next layer of cake on top.
Continue layering the cake and the buttercream, being sure to line up the layers so that they don't stick out further on one side. Once you place the last cake layer, smooth on a thin layer of buttercream as a crumb coat.
Chill the crumb-coated cake for 30-60 minutes. Then add your final layer of buttercream all over the outside of the cake. Smooth the sides with a pastry scraper.
Chill the cake again to set the buttercream and decorate as you like.
This cake will keep, wrapped well, for about a week in the refrigerator. I recommend keeping it at room temperature only for about 30-60 minutes before you serve it (unless you like to eat it cold, which is great too!)
You can also cut pieces, wrap them individually and freeze them in an airtight container.