Welcome Beauregard (beautiful name choice by the way)!!
I am glad to see another linnie fan here!! As Rozalka said, two inos must not be bred as they have a too much recessive genetics which means a narrow pool of genes. Rozalka is also right that this apply to parrots in general, not just linnies.
Unfortunately pairing linnie mutations is not that easy as it is for other parrots. If one pair mutations that should not be paired together he or she might end up with weak chicks with feather malformations and back toes flipped to the front.
Maybe that is the reason so few people have linnies and even less people is willing to talk about and teach newcomers.
I am in the same page as you are. I have had budgies and lovebirds for many years, but have adopted a pair of linnies only a few months ago. They are really fun and very much different than any other parrot you might have come across!!
As long as my mild understanding is, we should not pair together two ino birds, two greywing birds, one ino and one greywing, two birds carrying double dark factors (that are the birds with dark colors as the mauve, olive green and cobalt blue).
Regarding the lime green you said you have, it is a mutation I know little about. Maybe it is a way to call for a green greywing single factor (greywings can be single or double facotrs) or just another mutation not greywing (which I hope so if you are willing to breed them in the future).
If you could provide a picture, it could help me to have a better look.
In my case, I adopted a pair of greywings that I came to identify as so just last week, which means no breeding possibilities for me.
Cheers
