Interestingly, the mechanism that causes LDL to go down with proper treatment is the same with both thyroid and statins (at least from what I understand). It's the upregulation of the LDL receptor on your cells.
Statins cause a cholesterol deficiency in your cells by interrupting their process for producing cholesterol locally, which makes them express the LDL receptor to get more out of the blood. This also causes all the terrible side effects that many people experience like myalgia, rhabdomyolysis, and cognitive problems. Reading this makes me NEVER want to take statins: How Statins Really Work Explains Why They Don't Really Work.
I am not sure about the mechanism, but raising T3 if it is low causes increased expression of the LDL receptor also, without first causing a cholesterol defeciency in the cell since it's not breaking the cholesterol synthesis pathway.
If it does happen to be thyroid related, Chris Kresser has several excellent posts on the subject of thyroid health.