Hi there, all offspring will be Ino. Lutino is green with Ino and Albino is blue with Ino. If the hen is green/blue then you could get both blue and green Inos - Albino and Lutino. If she is not split for blue then you will get all green Inos - Lutinos, all will be split for blue.
Nope, sorry guys. You can't predict what colour the different sexes will be with this mating. In fact you can't predict whether a budgie will be male or female based on its base colour of blue or green at all with budgies. The inheritance of blue or green is not sex-linked.
Albino and Lutino are the same variety, Ino, just the green or blue versions. So all the chicks will be Inos. Whether a budgie is green or blue is completely unrelated to the sex, so whether the males or females are Albino or Lutino is completely unrelated to also.
The blue or green genes are not on the sex chromosomes with the Ino gene, so you wouldn't include them with the X and Y when working out the results. Each chick will receive either blue or green independently from the sex chromosomes and so independently from their gender.
I hope that makes sense, it feels a bit garbled to me but that's about how well my brain is working today...
The blue or green genes are not located on the sex chromosomes so are not passed on with the Ino gene. the Punnett square for this mating will need two squares, one for the sex-linked genes and one for the recessive genes.
Albino male = Xino/Xino (on the 2 sex chromosomes), and bl/bl (on 2 other chromosomes)
Lutino female = Xino/Y, and either Bl/Bl (df green) or Bl/bl (if the hen is green/blue)
The genes for green or blue are not linked to any other variety genes that I know of, so they are always passed on to the chicks randomly with no way to predict male or female by whether they are green or blue series (ie lutino or albino).
For sex-linked varieties like Ino or Opaline you can sometimes predict the sex of the chick with that variety, but not what the sex will be based on body colour (green or blue series). The colour is passed on completely separately from the variety.