Preheat oven to 375 degrees.
In a large bowl, mix together lemon cake mix, 2 eggs, 1/3 cup vegetable oil, and 1 teaspoon lemon juice.
In a separate large bowl, mix together strawberry cake mix, 2 eggs, 1/3 cup vegetable oil, and 1 teaspoon lemon juice.
Cover bowls with plastic wrap and place in the fridge for 15-20 minutes to let the dough firm up.
Remove bowls from fridge and roll 2 teaspoons of dough from the lemon cake mix bowl into a ball. Do the same with 2 teaspoons from the strawberry cake mix bowl. Carefully roll the balls together so that the cookie is half yellow and half pink.
Place the dough on a baking sheet lined with parchment paper or a silicone liner. Repeat all the steps until the baking sheet is full.
Bake cookies for 9-10 minutes (being careful not to overcook) and remove cookie sheets from oven. Let cookies stay on the pan for 2-3 minutes, then move to a cookie sheet to full cool.
While cookies are cooling, place 1/2 cup powdered sugar in a bowl and gently "dip" the top of each cookie in the powdered sugar (tap cookie on the edge of the bowl if it gets too much powdered sugar on it).
After cookies have cooled completely, mix 1 cup powdered sugar and 1 Tablespoon lemon juice in a bowl. Use a spoon to drizzle lemon glaze over each cookie (you can make the glaze thicker or thinner by adding more lemon juice or more powdered sugar).