Place the shortening, lemon juice, and vanilla in an electric mixer fitted with the whisk attachment. Beat on high speed until very creamy. Turn off the mixer, add the powdered sugar and beat until combined (start with the mixer on low and gradually increase the speed.) With the mixer running add the rice milk, 1 tablespoon at a time until the frosting is creamy and spreadable. Once the desired consistency is achieved, beat on high speed for 1 minute.