How can a person try to lower both cholesterol levels?

Many ways: When you say "both cholesterol levels", there's actually 3 main ones. Aerobic type exercise and a healthy diet, low in calories, low in fat and high in fruits and vegetables and lean protein will lower your bad LDL and bad triglycerides and raise your good hdl. Medication can also have good effects on these cholesterol components also.

Thyroid and Gall bla: Healthy thyroid function will normalize cholesterol. Always check thyroid with cholesterol levels. To lower LDL need anti/ inflammatory agents like vitamin e, niacin. For HDL cholesterol need carnitine atleast 2gm per day ( this will also normalize triglycerides).