HypoT affects LDL more than HDL. It has that effect because the body's elimination systems are so sluggish that the LDL isn't excreted like it should be.
Just before I was diagnosed hypo, I tried diet and exercise to lower my elevated LDL... even though my diet was already very good. I was easily able to raise the HDL with exercise, but the LDL actually went up a few points even with all that effort. I haven't had my cholesterol checked since I've been in treatment, but my doctor assured me the marginal elevation I had would be corrected with proper treatment.
Triglycerides may or may not be affected by hypoT; I was also able to lower those by drastically cutting sugar intake. Presumably, the exercise also helped.