It may and it may be more evident in the weight loss phase that usually comes about when you start a LC diet.
Some people report higher some report lower.. a better question might be "does it matter"?
For me, my cholesterol went up a little bit as I was losing weight, but it was temporary. From what I understand, there's loads stored, and as weight drops, it ends up in the bloodstream on the way out. So that'd be a good thing. Right now my total cholesterol is *slightly* elevated, but the ratio's are neigh on perfect, so nothing to worry about. All in all, most (80%) of the cholesterol in our bloodstream is made by our own bodies, the rest is nutritional. So... Considering I eat lots of eggs, and bacon twice daily... And lost 25 kilo's, and normalised my bloodsugars, and have lower cholesterol than I had when diagnosed and on statins... I'm an advocate.
Personally I’m only interested in inflammation and triglycerides. I couldn’t give a hoot about my general cholesterol numbers unless someone can show me that I have wayward pattern-B LDL and C-reactive protein, which I doubt.