A lutino budgie is ultimately a green series budgie. The Ino gene removes all the melanin from the feathers making the green turn to yellow, the black eyes turn to pink as well as the feet and tongue which will be pink and the beak will also have a lighter colour close to orange.
It's best to think that green is dominant to blue in order to avoid confusion.
From that pairing you would have 100% green series, yellow based chicks.
Lutino is a sex link mutation, so if you have a female visual lutino and a normal green budgie, all chicks would be green like the father and the male chicks will carry the Ino gene (that makes lutinos/albinos) from the mother and later on these males would be able to produce a few visual lutino females if paired with a mate of a normal mutation.