In a medium bowl, whisk 2 eggs, 1/3 cup oil, 1.5 teaspoons lemon juice. Stir in lemon cake mix. Mix until combined; set aside.
In a separate medium bowl, whisk 2 eggs, 1/3 cup oil, 1.5 teaspoons lemon juice. Stir in strawberry cake mix. Mix until combined; set aside.
Refrigerate doughs at least 30 minutes.
Preheat oven to 350 degrees F. Line a baking sheet with parchment paper; set aside.
Generously sprinkle 2 separate large plates with powdered sugar.
Working with the lemon dough first, scoop 1/2 tablespoon dough and place on powdered sugar plate. Repeat until you have enough to fill the cookie sheet about. Roll dough between hands then place back onto plate.
Scoop 1/2 tablespoon strawberry cookie dough onto second powdered sugar plate. Roll dough balls. The powdered sugar on the plate should make working with the dough easier when it's ready to be rolled. If it's still too sticky to roll, sprinkle a little powdered sugar on hands.
Roll 1 lemon ball and 1 strawberry ball together. Cup hands and apply a little pressure while rolling until smooth ball forms.
Place on baking sheet 1-inch apart. Sprinkle with a little powdered sugar.
Bake in oven for 10-13 minutes or until slightly golden around the edges. I baked mine for 12.5 minutes.
Refrigerate remaining dough in between uses.
Transfer baked cookies to cooling wire rack. Repeat with remaining dough.
To make the glaze, combine 1.5 cups powdered sugar with 2 tablespoons water or lemon juice. Mix until smooth. Using a spoon, drizzle glaze over cookies.