Use a hand mixer or whisk to cream together the butter and sugar in a bowl until light and fluffy, about a minute.
Add the lemon juice, lemon zest and pure vanilla extract to the bowl. Beat together until well-incorporated.
Add the rice flour and all-purpose flour to the bowl and beat briefly with the electric beater.
Gather the cookie dough into a ball, wrap tightly in cling wrap, and refrigerate. After 30 minutes remove the cookie dough from the fridge.
Preheat the oven to 350 degrees Fahrenheit/180 degrees Celsius.
Dust a surface and a rolling pin with powdered sugar and roll out the refrigerated shortbread cookie dough to a thickness of ¼th of an inch.
Use a cookie cutter to cut out square or round shapes or any shape you desire. I used a 2-inch square cookie cutter. Gather up any scraps, pat into a disc, roll, and cut out more cookies.
Place the cookies an inch apart on a baking sheet and bake 20 minutes or until the cookies are just beginning to color very lightly at the edges. Smaller cookies will need less time.
Place the cookies on a wire rack so they can cool down and firm up further. After 15 minutes, use a thin spatula to transfer the cookies directly to the wire rack where they can continue cooling.