Triglyceride Lowering Diets: In your journey to a better health, there are quite a few food types to favour, which would help in your triglycerides lowering diet. Vegetables In Triglyceride Lowering Diet: Most vegetables are not limited. One dark-green (string beans, escarole) or one deep yellow (squash) vegetable is recommended daily. Cauliflower, broccoli, and celery, as well as potato skins are recommended for their fiber content. This version is the first release on CNET Download.com.