The most likely outcome of such a pairing would be visually normal (green) offspring. Both blue and lutino are recessive mutation, so some of the babies will be split to lutino or blue, but none will be visual, unless the lutino hen is carrying a hidden blue gene or if the male is secretly split to lutino, in addition to blue. If you want more lutino birds, you will want to pair her with a male lutino or a bird that is split to lutino.
I have found conflicting information regarding the genetics behind lutino coloring in quaker parrots. It sounds like there might be two different mutations that can produce lutino birds - one follows autosomal recessive inheritence and the other is a sex-linked recessive gene. It sounds like the sex-linked mutation is more common, but I could be wrong.
Regardless, you won't be able to produce any lutinos from a lutino hen without a male that has at least one copy of the same mutation. Mixing birds with unrelated color mutations will generally get you right back to wild-type (normal green coloring), since the majority of color mutations are suppressed by the normal coloring. In other words, the offspring must have two copies of the mutated gene to display the unusual coloring. If they receive one mutated copy from their mother, but they get a normal gene from their father, the normal gene usually "wins" and that is what you will be able to see.
