Are eggs bad for the liver? My 5yo likes to eat eggs - he would eat 4 eggs a day. Is feels too much.

No. Eggs are an excellent source of protein, vitamins, minerals, and even cholesterol (all of us need some cholesterol). But, like any food, moderation is key. Eating one to two eggs per day has been shown to promote healthy weight loss and has a beneficial effect on blood cholesterol.
That is too much. Eggs are not directly harmful to the liver, but feeding a child as many as four eggs daily imparts a lot of fat into the diet, and there is something called "fatty liver" that can effect this child in the long term. Please limit egg intake to only two or three weekly. Kids still have to eat healthy.