>>>It seems the chazal allowed it because they thought lice do not come from male and female, but come from dirt or dust, which has been proven to be incorrect by modern day research.
Chazal talk about the eggs of lice too. (ביצי כנים)
To give but one example ונעשה אבימלך וכל נקבות ביתו אפילו עד ביצי כנים עקרות (Pirkey D’Rav Eliezer 26:8)
Lice do not need to mate continuously to lay fertilized eggs that will hatch. One mating lasts for a life time. Therefore their reproduction is considered being created from the dirt they live on from an halachic status.
The above is but one of the many approaches to this question. Experience has taught me not to discuss this online or it will attract OTD proselytizers like flies to manure so I will post further on this thread