Preheat the oven to 350 degrees.
In a medium bowl, cream butter, shortening, and sugar with an electric hand mixer or stand mixer. Beat in eggs. Add lemon juice and lemon zest.
In a separate bowl whisk flour, cream of tartar, baking soda, and salt together.
Combine flour mixture with wet ingredients.
Scoop cookies, using a medium cookie scoop, and place them on baking sheets lined with parchment paper (I usually bake 6 cookies per sheet).
Bake for 10-12 minutes.
While cookies bake, let's make the glaze! Add all lemon glaze ingredients to a small saucepan. Heat and stir until the butter melts, the sugar dissolves and the glaze is smooth and creamy.
Allow cookies to cool for 3 minutes before transferring them to a wire rack.
Brush cookies with lemon glaze and add a slice of lemon as a garnish.