Between two large mixing bowls, pour one box of cake mix into each bowl. To each bowl of cake mix, add 2 eggs, ⅓ cup vegetable oil, and 1 tsp lemon juice. Mix the batter in each bowl until smooth, combined, and free of lumps. Allow the dough to chill in the refrigerator for at least 15 minutes.
While chilling, preheat the oven to 375°F and prepare baking sheets. I prefer jelly roll pans lined with parchment paper or you can grease sheets with cooking spray.
In a bowl, add 1 cup of powdered sugar. Take the bowls from the refrigerator and roll a small bowl of strawberry dough (about 1-2 tsp depending on size of cookies you'd like) and repeat with lemon dough. With the two in your hand, roll the dough into one piece with strawberry on one side and lemon on the other. Gently roll each ball in the powdered sugar and place on the baking sheet. Repeat until all cookies are finished and on the baking sheet with about 2 inches between each cookie. Between baking, keep the dough chilled in the refrigerator.
Bake the cookies 8-10 minutes on the middle rack in the oven. Keep a close eye as the cookies bake fast. Remove from the oven and let cool.