Low-carb diets tend to improve the cholesterol profile by increasing levels of the “good” HDL cholesterol, and decreasing levels of harmful triglycerides. These are both good changes, associated with improved health.
Regarding the “bad” LDL cholesterol, most people experience no significant changes on low carb. However, some people can lower or (more often) increase LDL levels somewhat. Note that studies show that at least people over 60 years of age tend to live longer with higher LDL levels.
Taken together, studies show that low-carb diets generally improve risk factors for disease, including cholesterol. For a small minority of people however, cholesterol may go up abnormally high on an LCHF diet. In those situations it could be worth adapting the diet to normalize the cholesterol levels.
The bottom line: Low-carb and high-fat diets on average improve the cholesterol profile and reduce most risk factors for disease. The effect of this has been demonstrated in a 2010 study that showed a reduction in atherosclerosis after two years on a low-carb, high-fat diet.