Treatment with a medicated lotion, shampoo, gel, or cream often works very well to kill both lice and eggs (nits), but no treatment is 100% effective. It is possible that if some eggs survive treatment and are not removed from the hair, they may persist or spread to someone else.
You may wish to remove eggs for cosmetic reasons. Also, some school districts have a "no nits" policy that requires that children be free of eggs before returning to school.
Eggs stick to the hair and can be difficult to remove.
Citations
WebMD Medical Reference from Healthwise