Are hypothyroidism and hyperlipidemia related?

Yes. Your metabolism is slower with hypothyroidism. This will slow down your body's ability to clear or break down cholesterol effectively, leading to higher cholesterol level.
Yes. Hypothyroidism is associated with increase in blood lipids, including cholesterol.
Mixed hyperlipidemia. People with hypothyroidism can have a mixed hyperlipidemia with elevation of both cholesterol and triglyceride. Once this is adequately treated with levothyroxine, however, the thyroid-related component of the hyperlipidemia should be eliminated.