How do you naturally lower the level of triglycerides?

Diet, avoid alcohol. Low carb diet, eat oily fish, avoid alcohol, lose weight, and control diabetes if present.
Low carb diet. Eat only meat or fish or cheese or eggs or poultry and low starch veggies, drink only water. In other words avoid all carbs, carbs will only briefly raise your sugar levels and then you will get hungry again. The fats in the meat or fish or cheese or eggs or poultry will act like a "log on your metabolic fire" to keep your blood sugar stable for hours. Healthy blood sugar 90-99.
Diet. Along with weight loss, exercise, alcohol in moderation and control of blood sugars if diabetic.