A few years ago my husband was warned his cholesterol was way too high even though he was slightly underweight (and quite lean at the time). He was consuming a lot of eggs and whole milk and was told to cut way back on those. For a while he drank exclusively plant milk, and his egg consumption dropped to less than 2 per month. He has been eating far more vegan meals at home (always homemade rarely processed give or take a few items like the plant milks or tofu to an extent is processed). Recently his cholesterol was checked again and it dropped from 190 to 116. His LDL went down to the mid 60s, though HDL could be a little higher (was 39 and similar to before). I have been pushing him now to eat more leafy greens and nuts/seeds. My husband does tend to eat more processed foods but also some healthy food that I make him.
In 2012, two years in as a vegan, I had a fasting cholesterol/glucose etc test done. I used to eat very healthy as an omnivore, very little processed food, very little dairy (body couldn't tolerate it), lots of fish and some eggs. I eat even healthier as a vegan. At any rate, my total cholesterol went from 155 (tested as an omnivore in 2010) to 125 in 2012 as a vegan. As a vegan my triglycerides were 27, fasting glucose 88, LDL 62, HDL 57. The only better number I had as an omnivore was the HDL which had been 62, and I presume it was because of the salmon and sardines I used to eat a lot of. Regardless, my fat intake as an omnivore was still only about 20% and as a vegan it seems to consistently fall to about 15% when I check food intake. I have never been remotely overweight and have always been on the low side of normal or else underweight, but I have worked hard to stay there (I am in surgical menopause and have had hypothyroidism for 27 years so I can both lose and gain weight easily). I am very active, 43 years old, and look half my age. I feel so much better and have increased energy and better digestion when I don't eat meals that are heavy in fat. But I feel that a little fat gives me the extra oomph for doing activities like paddling a canoe long distance, lifting weights (or my canoe), gardening etc.
I also don't understand the OPs interest in consuming eggs if they are trying to go low fat (I think it was another thread this was talked about). Eggs are a huge source of saturated fat unless one consumes only the egg white and wastes the yolk (which is where most of the nutrition in an egg is). Beans, whole grains, tofu and tempeh, green vegetables, some seeds like chia or flaxseed are excellent sources of lower fat protein. Most are very cheap except maybe the tempeh and seeds/nuts. Pumpkin seeds tend to be much cheaper than some of the others. Flaxseed isn't too bad either.