I really don’t want to get involved, but I do have a point to make.
If lice are hatched from eggs, then how do we attribute kessamim? The entire concept of teliya is based on abiogenesis.
No, they were most definitely not talking about lice coming from eggs. A better possiblity is that what we call lice is not what Chazal called lice, and we in fact have no idea what Chazal lice are. I say better, only.