Preheat the oven to 350°F.

Line two 12-cavity muffin pans with paper liners. Set aside.

Place the butter, canola oil, granulated sugar, vanilla, and lemon zest in a large mixing bowl. Reserve the lemons for later use. Using a hand mixer or stand mixer fitted with a whisk attachment, cream ingredients together on medium speed until smooth, about 1 minute. Add the eggs and continue to beat until mixture is light and fluffy, about 1 minute longer.

Sift the flour, baking powder, baking soda, and salt into the bowl. Pour in the lemon juice. Beat the mixture on low until ingredients begin to come together. Slowly stream in the milk and continue mixing, scraping down sides of bowl with a rubber spatula as needed, until a smooth batter forms.

Divide the batter between the prepared muffin cups, filling each liner no more than 2/3 full.

Bake the cupcakes on middle rack of oven until a toothpick inserted in centers comes out clean, 18-21 minutes.

Check to see that cupcakes are done. Remove from oven or add time as needed.

Allow the cupcakes to cool to room temperature before frosting.

While the cupcakes cool, make the frosting. Place the butter, cream cheese, and lemon zest in a large mixing bowl. Beat with a mixer on medium speed until smooth and creamy.

Add the powdered sugar to butter mixture in two additions, beating on low speed after each until sugar is fully incorporated. Add the vanilla, heavy cream, and salt to the bowl. Continue beating on medium-high speed until frosting is light and fluffy, 2-3 minutes. Beat in more heavy cream if frosting appears too thick.

Pipe or spread frosting onto cooled cupcakes. Refrigerate until ready to serve.