I heard one finnish functional doctor talk about this and googled a bit.
"A consequence of hypothyroidism is a slowing of the body's ability to process cholesterol. This processing lag is largely explained by a reduction in the number and activity of LDL receptors, which have the function of helping metabolize LDL cholesterol. When the number of receptors decreases, LDL accumulates in the blood-stream, acting to increase both LDL and total cholesterol levels.16
Another reason for cholesterol increase is that hypothyroidism significantly alters the metabolism of steroid and other hormones, including their rates of secretion or production, plasma concentrations and plasma protein binding, flux through various compartments and rate and pathway of catabolism in the liver or other metabolizing tissues. These changes in steroid-hormone metabolism are attributed to the action of thyroid hormones on controlling various rate-limiting enzymes and to the concentration of critical cofactors in the metabolizing tissues.17 Consider that progesterone is synthesized from pregnenolone, which in turn is derived from cholesterol. Like-wise, vitamin D is produced through the action of ultraviolet irradiation (UV) on cholesterol in the skin, or more specifically, 7-dehydrocholesterol. Since hypothyroid-ism reduces the conversion of cholesterol into progesterone and vitamin D, more cholesterol is left metabolized, thereby contributing to total cholesterol load."