With regard to lice, the egg of a louse is called nit. Sometimes, some people confused nits with lice. Often, they talk about and search for lice treatment, lice products, a lice comb. Etc., while they really mean nit treatment, nit products, a nit comb. They are not the same. The infant lice will come out once the nits are hatched.
When the female lice lay their eggs, they also provide protection for them so that they will not fall of the body of their host. There are different ways through which different species of female lice do that. Some of the species of female lice will bond their eggs to their hairs of their host using a special kind of saliva. When the eggs are attached to the body of the host in this manner, it is very difficult to separate them from the body of the host unless with the application of special type of product.
There are other species of lice like the bird lice that protect their eggs by leaving them in the part of the body of their host that cannot be accessed by the preen. So, when the bird is preening, the nits will not fall off the body of their host. The eggs are pale in colour when they are alive. But they turn yellow when they are dead.
It will interest you to know that some species of lice are parthenogenetic. Parthenogenesis is a type of reproduction that does not involve fertilization of the female gamete by the male gamete. In this type of reproduction, the female gamete develops on its own with the male gamete fertilizing it into new individuals. Some species of lice are like that.