Doctor believes that by taking medication for lowering tsh we can also lower cholesterol and maybe stop taking cholesterol medication is this true?

Thyroid cholesterol: If you are hypothyroid (elevated tsh), normalizing the thyroid will help your cholesterol, sometimes quite a bit. But if your thyroid is normal (tsh in normal range) then adding more thyroid medication will not help your cholesterol.

Yes: Hypothyroidism often raises cholesterol and treating it will tend to bring it down to the healthy range.