I had elevated triglycerides when I went low carb - three months later they were fine, and my HDL, total and ratio cholesterol levels are good.
I was having 3 monthly blood tests, now 6 monthly.
I have double cream every day, full fat milk, real full fat Greek yogurt - and eggs or cheese (or sometimes both) most days.
You don't need to eat huge amounts of fat, unless you are underweight, but make sure they are 'good' quality unprocessed fats, is no vegetable oils.