By no means everyone sees their various 'cholesterol' scores improve.
A video posted on here recently (can't remember which one
, but it was talking about the Aussie cricket team and LCHF sweeping South Africa) quoted a figure of 75% had improved trigs and cholesterol on LCHF. 25% did not. without quoting the study this came from, I am wary of taking it as gospel.
Also, many people starting LCHF experience rises in their cholesterol - connected I believe, to the weight loss. A test during this period will give a very different result from when the person becomes ketoadapted. Consequently, medical professionals may see 'negative' results from the diet, and have all their fears confirmed - when in reality that score was a temporary one, before levels dropped. Not that I am convinced that a low score is better than a medium to higher score.
The only score I am interested in, is the Triglycerides - because of the implications for a fatty liver. The other scores can, in my opinion, do what they like.
Anyone with a familial history of hypercholesterolaemia should be closely monitored. And if they show symptoms, they will be receiving medication. I am unsure of the details, so cannot comment whether dietary fat intake makes a difference to their cholesterol scores. If it doesn't, the question becomes redundant. They are undoubtedly a special case, and really not relevent to a general discussion. Unfortunately, there is so much nonsense information around about dietary cholesterol. Thank heavens I don't have that condition because I would be totally distrustful of anything I was told, even by a supposedly knowledgable medical team.