Hanna, there are plenty of fruits you can eat that not only will not raise your triglycerides but can help lower them. The best fruits would be apples, pears, apricots, pomegranate, anything that is somewhat light and packed with fibrous material. Even though fruit like apples have a high concentration of various types of sugars in them, the bitter and astringent tastes, phyto-chemical and fibrous materials, work in a synergistic way to be extremely beneficial for the human body. A lot of nutritionists and doctors don't understand the synergistic ways that foods work as a whole and just look at the about of sugars/carbohydrates/protein, etc., looking at only macro-nutrients in this way gives a very skewed and incomplete picture of what is going on. Realistically, most fruits will be helpful; the only ones you need to avoid are really heavy fruits like bananas, dates and maybe some others. I think an orange a day eaten whole, not orange juice would be okay but you won't be getting loads of vitamin C from one orange obviously.