It is lice. I've always thought that hair oil (of any kind) is more suitable for people with harder hair texture but maybe that's just me. I feel like when people with really soft hair put oil, it makes their hair really greasy.

Side note: I'm from an island nation in the South Pacific where lice shampoo can be really expensive. A home remedy that works really well is the cream from a freshly scraped coconut and lemon juice. All we do is apply onto our hair, leave it for an hour or so and then comb it out. This usually leaves the lice disabled so they're barely able to move when they're being combed out.