"I am an Irish native and an American citizen.  I have been living in the U.S. for eight years – I got my green card through the visa lottery.   Before I came here I had a relationship at home and I fathered a son who is now 11. His mother and I are on good terms; she never married and is thinking of coming here as she recently lost her job in Ireland.
“I am wondering what I can do to help facilitate this.  Because I am a citizen I presume I can sponsor my son for a green card? And even though we are not married, is there anything that I could do for his mother, sponsorship-wise?  Marriage isn’t on the cards for us, but we are close and share a child and would like the chance to raise him together. I know this sounds strange, but I would really appreciate your advice.”

It doesn’t sound strange at all, but unfortunately there isn’t much that you’ll be able to do for your former girlfriend as far as sponsorship and legalization goes.

As an American citizen over the age of 21, you have the right to sponsor parents, minor children and a spouse.  Immigration law doesn’t provide for your particular situation, even though your ex is the mother of your child.

You would definitely be able to sponsor your son for permanent resident status as it seems that you’ve maintained a close relationship with him – a key component for fathers wishing to sponsor children born out of wedlock.

You will have to show that you “legitimated” your son, which is a formal recognition of your relationship with him.  How to do this?  Presumably your name is on his birth certificate, and you’ve also presumably provided financial and other support as he’s grown up.

When you’ve established legitimation, which shouldn’t be difficult in your case as you remain friendly with your son’s mother, you would be eligible to petition for his green card as an immediate relative, which means the wait time would be in months rather than years. 

But this doesn’t solve the problem about his mother’s legal status here.  You don’t provide information about her background – does she have a university degree, or a specialized skill that she could possibly lead to a sponsored job here?

If she doesn’t have a U.S. citizen relative to sponsor her for a green card then she’d have to find an employer to act on her behalf – a time consuming, difficult and costly undertaking.

She could apply for the annual visa lottery later this year, and perhaps she would get lucky as you did – but that’s a long shot at best, and not a plan that should be banked on.

You say that marriage isn’t happening, but if at some point you/her had a change of heart you would be able to sponsor her for a green card as an immediate relative, and she’d have a green card in a matter of months.  By far that’s the quickest and easiest option to obtain legal status for her – but, of course, it’s a big personal decision that the two of you would have to make.