Preheat oven to 350 degrees. Line a standard muffin pan with cupcake liners.
Combine the rice milk with ¼ cup lime juice and vanilla. Let sit for 5 minutes. It may look curdled, that’s ok.
Whisk together the flour, baking powder, salt, and baking soda.
In an electric mixer, fitted with the paddle attachment, cream together the ½ cup shortening with the ¾ cup sugar. Beat in the eggs, one at a time, mixing well after each addition. Beat in the lime zest. Turn the mixer to low, add half the flour, the milk mixture, then the rest of the flour, Mix just until combined. With a spatula, scrape the sides and bottom of the bowl and make sure the batter is well combined. Divide the batter among the prepared muffin cups. Bake for 20 minutes or until a toothpick inserted into the center comes out clean. Brush the tops of the cupcakes with tequila if desired. Let cool in the pan for 5 minutes then remove to a wire rack to finish cooling.
While the cupcakes bake and cool, make the frosting.
In a mixer preferably fitted with a whisk attachment, beat together the shortening, 2 tablespoons tequila, lime juice, and lime zest. Add 3 cups powdered sugar and beat, starting at low speed then raising to medium-high until smooth and the consistency of buttercream. If too soft, add more powdered sugar, at little at a time.
Frost the cooled cupcakes and garnish with lime zest and a lime slice.