My surgery tried to put me on statins when my cholesterol was at 5.8 (I wish they had instead informed me that me blood sugar was approaching pre-diabetic, but that's another story). They like the ratio of your cholesterol to be lower that 4 to 1. The best response I had to cholesterol numbers was going LCHF, especially when I started eating more Salmon and Mackerel, current total cholesterol 3.99, with a ratio of 1.97 to 1. So for me LCHF (along with exercise) has improved my figures by over 30%.
I think lowering is due to the version of LCHF selected, as this is a broad church (I don't have proof for this). I eat 35 grams of porridge oats (some type 2's can't tolerate this), nuts, seeds, berries, fish, meat (not so much) and reasonable cheese.