I had a total thyroidectomy due to cancer. my lab shows low tsh but t4 and t3 (liothyronine) levels are normal indicating correct dosage why would my tsh be low?

Low TSH: Low TSH should be respected and you may need adjustment of your medication. Seeing your Endocrinologist may be needed, and they can discuss if a dose change is needed. T3, (liothyronine) T4 don't always paint the full picture and have to looked in context of your symptoms, TSH.

May be just right: A low TSH with normal T3/T4 levels means that while these T3/4 levels may be just right for someone else, they are just a little bit higher than what nature intended for you. BUT (and this is very important) in patients who've had thyroid cancers, doctors often want the TSH a little low. Ask your thyroid doctor where your TSH should be, and don't let any other doctors adjust your thyroid pills!

TSH: TSH may be low simply because your thyroid meds are doing enough to keep the TSH at a low level. If you are feeling OK just relax and enjoy life!