If you have a normal TSH and T4 levels but your T3 (liothyronine) is low do you need to increase levothyroxine?

Depends. The T3 (liothyronine) may be low before you take your medication and isn't necessarily abnormal. If you still have symptoms and the TSH is not in the low part of the normal range then adding more levothyroxine is probably the right thing to do. Some people do not convert enough of the T4 to T3 (liothyronine) and they need to take some T3 (liothyronine) in addition to T4 or take a natural thyroid med like Armour Thyroid or nature-throid.