The short answer is probably not, nor is it a really good idea.
If you want a good outline of the history of our current nutritional dogmas, permit me to recommend two books: Good Calories, Bad Calories, by Gary Taubes, and The Big Fat Surprise, by Nina Teicholz. (The second book goes by a different title in Europe, but I don’t remember what it is, sorry.) I like these books because they cite extensively from the scientific literature, and they show how our fear of saturated fat was created mostly out of whole cloth, partly from the influence of economic interests and partly out of scientific ego.
Okay, so now you don’t need to read the rest of this post. But I’ll leave it, in case you’d rather not run right out and buy those books, lol!
However, while you could use vegetable oils instead of animal fats, they are likely to make you queasy, and there are health consequences to consuming all those ω-6 fatty acids. At the very least, stick with the fruit oils (avocado, coconut, olive, and palm) and avoid the industrial seed oils (soybean, canola, cottonseed, corn, cornflower, sunflower, etc.), which are much lower in ω-6.
The fear of saturated fat is actually not well-founded on data. In fact, a number of large, well-funded studies done to provide such data ended up showing exactly the opposite. Lower cholesterol is associated with increased rates of cancer, lowered immune system activity, and a host of other problems. People past a certain age, especially women, tend to live longer and be healthier, the higher their LDL is.
A number of studies assessing cardiovascular risk say that the correlation between LDL and cardiovascular risk is negligible, but the ratio between triglycerides and HDL is actually quite a strong predictor of risk. So in European units, you want your ratio of triglycerides/HDL to be 0.9 or less (in American units, it’s 2.0 or less). Alternatively, your doctor could order a nuclear magnetic resonance (NMR) analysis of your LDL, and if you have the healthy Pattern A, your cardiovascular risk would be minimal.
So it sounds as though you are fine. If you’d like to post the actual test results, we could look them over (if you post a scanned image, be sure to block out all the personal information first!).
And actually, on a low-carb, high-fat ketogenic diet, most people’s LDL comes down. There is a specific group of people whose LDL goes up instead, but it has not been shown that high LDL on a ketogenic diet is a problem, so long as the ratio of triglycerides to HDL is good. (Be warned, however: do not get your lipids tested before you’ve been eating a ketogenic diet for at least six months, because tests taken before that point can look quite alarming. However, by six months, the lipid numbers will have settled down. That’s the point at which to freak out, if you need to, lol!)
There is a whole history to our fear of saturated fat. Some of the early evidence was distorted, and has been shown to be erroneous. But the fear has become so entrenched that everyone just “knows” saturated fat is going to kill us. But actually, a number of randomised, controlled trials have shown the opposite, in addition to the large epidemiological studies I mentioned earlier. The American authorities discovered, decades ago, that there is actually a significantly greater cancer risk from lower cholesterol, but they decided not to mention it, because they didn’t want to “confuse” the public.