Preheat oven to 350°F. Line cookie sheet with parchment paper.
Prepare strawberry cookie dough: To a large mixing bowl, add dry strawberry cake mix, melted butter, vegetable oil, and eggs. Mix by hand until well combined; the dough will be very thick. Stir in white chocolate chips.
Prepare lemon cookie dough: To a separate large mixing bowl, add dry lemon cake mix, melted butter, vegetable oil, and eggs. Mix by hand until well combined; the dough will be very thick. Stir in white chocolate chips.
Scoop out 1 Tablespoon of strawberry dough and 1 Tablespoon of lemon dough per cookie. Gently press the 2 scooped Tablespoons together to make a half strawberry/half lemon ball. Repeat for each cookie.
Place the cookie dough balls at least 2 inches apart on a parchment lined baking tray. Press a few extra white chocolate chips into the top of each cookie.
Bake in preheated oven for 10-12 minutes. The edges should be set, but the center of the cookies will look a little underdone. They will continue to firm up as they cool.
Let cookies cool undisturbed on cookie sheet for at least 10 minutes before serving. Enjoy!