the anti-egg campaign began in the 1960's, based on some rather squishy science that has long been overwritten with more accurate stuff. The fear was, eating the cholesterol in eggs would make your serum cholesterol go up, and that would "cause" heart attacks. Both assumptions are now known to be wrong.
1) eating cholesterol does not make your blood serum cholesterol rise (unless you have a rare disorder that in fact does just that). (Eating sweets doesn't make you sweet and eating fat doesn't make you fat, either! what simplistic or downright goofy equations those are.) 20% of the cholesterol in your bloodstream is from the foods you eat; 80% is manufactured in your liver in the presence of high levels of insulin. Thus, since LC is a insulin-control diet, you'll manufacture less, not more cholesterol.
2) cholesterol levels and heart disease...not a clear cut relationship there, either. Read Ravnskov's The Cholesterol Myth (part of it is on-line) for more on that. Even were their clear-cut correlations between high cholesterol and heart attacks (and those correlations aren't clear, actually), correlation does not equal causation. (wbahn explained this issue wonderfully in a recent post about elevation and SAT/ACT stores)
Eggs are something humans have been eating for as long as we have been human...and before that, even. Millions of years of reptile then bird eggs helped mammals survive, thrive, develop intelligence...and we are today, so "smart" that we outthink our normal and natural ways of eating.
Even the AHA has recently okayed eggs (years after they have been proven not a health hazard, but better late than never)
4 a day is plenty fine. I always say, though, to skip one day per week of every food we eat to avoid developing allergies. Chicken eggs are a moderate sort of allergen food (yolks, usually), so it seems worth the thought to me to take at least an egg-free day per week to help guarantee that I can continue to eat this yummy, versatile, and cheap source of high-quality protein.
Oh, and I do eat organic eggs from free-range chickens--better nutrients and better Omega 3:6 fatty acid ratios.
HTH