How to Dispose of Lunchables Email Lunchables are easy to pack for kids when you’re short on time, but how do you dispose of the packaging when you’re done? The cardboard sleeve goes in the recycling. The plastic wrap and plastic container go in the trash. They are not recyclable. If you want to cut back on the waste, try making your own “Lunchables” at home. You’ll save money, too. Check out the Squawkfox homemade lunch experiment to learn more.