Lifestyle/diet changes will only make a small difference if trying to reduce for most people.
That said, if you are on a keto diet and not massively overweight then adding carbs back in would reduce your cholesterol numbers more. People who are leaner (less heavy) tend to have larger cholesterol shifts with diet changes (look up Lean Mass Hyper Responders).
At one point my LDL was over 11.
Currently I am mostly high-protein, low carb and moderate fat diet. Eggs, Salmon, Avocados etc. My cardiologist has no issues with this and in fact had no issue with my diet when I was keto - that shows how little difference diet makes.
The best thing you can do that is not meds is stop eating refined carbs (which leads to higher blood sugar, higher insulin resistance, higher blood shear rate, more arterial inflammation and therefore ultimately more plaque) and do a good amount of exercise every day.
Look up the videos by Thomas Dayspring for more complex and mechanistic info. but LDL by itself is not thought to be the most important marker nowadays. Triglycerides (and ratio to HDL) is thought to be far more important as a risk gauge.
But with specific regard to LDL it’s best to know that it’s not the quantity/amount of LDL that matters most, it’s the number of particles because small particles of LDL are bad (small enough to go through the endothelium) but large particles of LDL are good (too big to go through the endothelium).
It is possible to get LDL sub-fraction tests (LDL-p) privately to test the particle sizes and counts, mine cost about £100 in London. It showed that whilst the simplistic NHS test said I had more cholesterol quantity than my cardiologist liked the more advanced private test showed I have practically no small LDL particles so my private cardiologist is happy. I had a costly private angiogram to check how little plaque I now have (having reduced it).
Remember that LDL is not a problem unless your arteries are damaged and LDL does not damage arteries. Smoking, high blood pressure, high insulin resistance and inflammation from too much blood sugar for decades are what damages arteries.
You can try Berberine supplement too to reduce cholesterol levels. Also, Niacin (flush-type) and high dose EPA fish oil (minimum 2g / day) have both been shown in good studies to reduce soft unstable arterial plaque.