Palm, coconut oil, and rendered fats such as lard are also fats that will raise triglyceride levels. However, substituting monounsaturated fats like olive oil and walnut oil can lower them. 3. Grapes. Eating candy and other sugary foods fuel triglyceride levels, but eating naturally sweet grapes can lower them. Grapes contain pterostilbene, a compound that acts similarly to ciprofibrate, a commercial product that lowers triglycerides, according to the USDA.