Indeed they will be all ino birds, lutino or both lutino and albino. It all depends on the genetic of the lutino.
Lutino are from the yellow series and albino from the blue series. Green birds are from the yellow series with the blue pigment, hence the green color.
The yellow series is dominant over the blue, but heterozygotic birds (yellow/blue genes) that will appear yellow or green, if paired might produce blue birds.
If your lutino has the blue series genes (not showing up obviously) you might have lutinos and albinos. If it is a homozygotic lutino (not having the blue series gene) all babies will be lutino (carrying blue series genes).
I might be wrong as it has been several years since I studied Budgies?genetics.
Please be aware that for many bird species, ino birds should not be paired together as they have a narrower gene pool and might produce offspring with even poorer genetics; sometimes with autosomal disorders. I don not know for budgies but for roseicollis lovebird it should be avoided.