High cholesterol should be unrelated to gluten intolerance, based on the currently accepted medical model. Let's take a little closer look at its function in the body.
It originates from two sources: it is consumed as part of the diet, and it is produced by the body. Consuming animal products has never been shown to directly correlate with arteriosclerosis, since entire cultures that consume large amounts of meats, animal fats,and other animal products (for example, the traditional French diet, and the traditional Inuit diet) have no widespread problems with arteriosclerosis or the other problems associated with a high intake of animal products.
It is also produced by the body in response to tissue damage. It helps to heal the damaged tissue by acting like a salve to soothe the tissue and like a bandage to protect it from further damage. It works on nerve sheaths, muscle tissues, connective tissues, bones, organs - including the brain, blood vessels, and the dermis.
The liver produces it, which enters the blood stream carried by low-density lipoproteins. Since the body does this when there is damage to repair, chronically high LDL levels mean chronic damage.
When it has done its job and the tissues are healed, it is attached to high-density lipoproteins for its ride back to the liver, where it is broken down and ultimately excreted. High serum HDL levels mean that the body has mostly healed, and no longer needs it.
As you can see, the common references to HDL cholesterol as "good" and LDL cholesterol as "bad" are simplistic and misleading. It is a bad sign if your body is producing a lot of low-density lipoproteins, because that means you have a lot of tissue damage somewhere; however, taking drugs to destroy some some of these compounds means that the damage does not get fixed. It amounts to shooting the messenger.
The better response is to question where the damage is located, and what is causing it. Instead of trying to change the quantities of a marker, change the actual cause of the damage. When the damage stops, the production of low-density lipoproteins, high-density lipoproteins, cholesterol and triglycerides all drop to normal levels, naturally.
This brings us to the relation between gluten intolerance and high cholesterol. Untreated non-celiac gluten intolerance does cause tissue damage over a long enough time frame. Other food and environmental intolerances, sensitivities, or allergies can also cause tissue damage if left untreated, so these should also be investigated.
If you are gluten-intolerant, your body may be producing large quantities of LDL and cholesterol to heal the damage. Getting off all gluten will allow your body to heal itself because the irritant is no longer present, and your serum cholesterol levels will gradually return to normal. If they don't, either you are still consuming gluten somewhere (cosmetics? lotions? vitamins?) or you have other sensitivities you need to identify and rectify.
I have seen my own chronically high levels drop to within normal parameters after going completely gluten-free. It took most of a year for the chronic damage to heal, but my numbers have remained normal for four years now. This is of course merely empirical evidence, but it is strong enough evidence for me to tell you to talk to your health-care provider about doing a gluten challenge, and ultimately getting off statins with his or her supervision.
It is most definitely in the best interest of your health to find the cause of the damage your body is trying so hard to fix for you. Always, always, always look for a cause, not just a symptom - or in this case, a marker of a symptom.