Would it be considered important to remove old lice eggs from hair?

Lice eggs. Lice eggs need warmth to hatch. So all nits on the hair less than an inch from the scalp should be removed. Beyond an inch, the nits have either hatched or contain unhatchable eggs. However, for cosmetic reasons, remove the nits as they cause white specks that are easily visible especially on black hair.
Yes! Lots of work but totally worth it. After you treat your scalp with medicine, rub conditioner or olive oil into your hair. Use a nit comb or a sturdier flea comb for cats & dogs. Comb through hair every 2-3 days to remove nits and lice. It's important because the treatments don't kill all the lice. So nit-picking helps get rid of them & prevents a whole new crop from bugging you.
Nit Removal. If you read the fine print on most over-the-counter lice treatments, you will see that the recommend manual removal of the lice nits is more important than the shampoo or other treatments. Why? Because most of the treatments that you will buy only target the adult lice. So if the lice nits remain, they will start to hatch and grow into adult lice that will in turn lay more eggs.