If the thyroid hormone levels are normal, there is no impact on trig levels -- but if under-replaced (ie, high TSH levels) then trigs can increase. Sounds like he is prone to high trigs anyway -- low sugar/carb and low saturated-fat diet along with exercise can help
Yes, I believe the exercise would help along with a healthy diet. But are the thyroid hormones all within a good range? Also, does he feel good on the level if Synthroid he is on.