That doesn't look like a lavender chick to me. Lavender(on an otherwise black chicken- a solid lavender that is) has a very even effect on their color. Try doing image searches for (solid)lavender chicks, the down is exactly the same shade all over.
I'm pointing out the solid lavender as lavender over other color patterns can give seemingly uneven coloring on chicks, like porcelain, lavender on a red duckwing pattern etc.
Blue on the other hand is extremely variable, even on solid black chickens and chicks. They are rarely very even all over, example blue roosters typically have much darker necks and backs than their bodies- that does not happen on lavender roosters. That chick shows uneven coloring in the down is the reason I don't think it;'s a lavender.. I can't tell by picture if it's a blue or a black... you'll find out soon enough once the feathers grow out.
Yes- lavender bred to lavender split= half and half of each. If you like the white hen enough, you can test her genetics by breeding with a lavender rooster and see what happens. If you hatch more than 10(more is better but lets be realistic) and none turn out lavender, it is strong proof she is not lavender.
Test matings are a great way to get rid of hidden genes. If you really do not want lavender, ever, it could be useful to either get or keep a surprise true lavender around as a tester to cull out the hidden carriers. Lavender roo to test the hens, lavender hen to test the roosters(a reason for keeping the white hen if she proves to be lavender?).