General reports here are that LCHF will raise your total cholesterol (TC) but improve your triglycerides and ratios. TC is not statistically significant at predicting anything and shouldn't be used as a diagnosis in itself, just as a hint to run more detailed lipid tests.
Having said that there are a not insignificant number of people on here reporting lipid profile problems on LCHF that are worrying (not just high TC). It may be down to individual differences. It may be the "quality" of the fats is important rather than the quantity. It may be that higher amounts of omega 3 EFAs required.
I think it would be prudent to get regular full lipid profiles done while doing LCHF.
LCHF will not work if you use low fat products or avoid fats. There is no evidence demonstrating saturated fats are bad for health. Quite the contrary in fact. But it may be a good idea to mix in high quality mono and poly unsaturated fats as well.
I totally get wanting to avoid statins if possible, but if he can't get his important lipid measures down by LCHF or other means he will come under great pressure to take the statins.