Regrettably, Eucalyptus, Rosemary and even Lavender all contain camphoraceous elements.
Lavender doesn't have as much as the other two. I am not sure about Tee Tree, but from the smell of it, I think it is also camphoraceous.
As RF wrote, you can use a base oil, such as Olive oil on her head overnight, wrapped in cling film or her head will get chilled.
Then wash out thoroughly in the morning. Repeat this nightly if necessary until all are gone. And check regularly with a nit comb.
Quassia spray is needed to prevent reinfestation. If you can't get Quassia, you can use a couple of drops of staphysagria mother tincture behind her ears every morning, also a 5ml bottle of staph tincture can be put into the hair rinsing water after each wash.

Homoeopathically, the classic remedy for nits is Staphysagria, or it can signal a need for Tuberculinum.