I have seen mentioned by others who have lost a lot of weight on LCHF that their cholesterol goes up for a while but then normalises. You could wait and see and read up on it in the meanwhile. As fas as I've heard there isn't really any hard evidence for the benefit of statins in women.
@Frodmella, Yes, cholesterol tends to rise when you first lose weight, but then it stabilises. My total and LDL cholesterol went up a lot in my first nine months on LCHF. After that they went down by 2 mmol. Google weight loss and cholesterol, and you'll find that's quite a common pattern.
After that on LCHF, while triglycerides continue to fall and HDL to rise, LDL tends to go down again, tho it often stays above the official targets.
You could try arguing that low trigs, high HDL and a good ratio between them, and also between HDL and LDL, is a better sign of cardiovascular health than presumed LDL (they don't actually measure it, just subtract it from TC).
You don't have to agree to take statins. I myself never would. No RCT has ever demonstrated lower mortality for women on statins (in fact the reverse), even in the badly flawed RCT reports we have. Ultimately it is your choice: if you wish, you can say No.
If an overview of the arguments required, download the Uffe Ravnskov book. I th it's The Cholesterol Myths that is now available free, because he just wants it read. Google it. He does seem to be a fairly reliable presenter of the studies.
Good luck.