Really, we'd suggest reading the sequel to this book, Son of a Witch, if you want the full measure of Liir's character and are interested in how he turns out.
Here, Liir is a sad, pudgy child. He's arguably one of the most pathetic figures in the book: his dad is dead and he doesn't even know who his dad is; his mother doesn't acknowledge him as her son; his half-siblings torture him; he nearly drowns in a well; and even the generally kind-hearted Sarima ignores him. The boy has a raw deal.
Liir is almost a moral barometer for everyone else in Kiamo Ko. As Nanny points out, everyone pretty much fails in the whole "caring for others" thing.
"Where does he sleep?" said Sarima.
They all looked at one another. The sisters looked at Elphaba, and Elphaba looked at the children. .. .
"He doesn't even have a bed?" Sarima coldly asked Elphaba.
"Well, don't ask me, this is your house," said Elphie. (188.8.131.52-44)
Liir's childhood suffering is downright Dickensian – he's like Oliver Twist or David Copperfield.
Aside from revealing a lot of unpleasant truths about the adults and kids around him, Liir also tells us a good deal about Elphaba's character. In a way, he's the ultimate product of Elphaba – alternately pathetic and mouthy as the novel progresses, and as he himself progresses from a child to a teenager.
But after suffering along with him as a child, we're actually glad to see that Liir is growing up into a snarky and rebellious teenager. It's also worth noting that he hasn't lost his inherent goodness and gentleness – check out his interactions with Dorothy to see what a sweet kid he can be.
Liir, who has the potential to become a really cool person, is still treated dismissively by Elphaba, even as he grows older. In a way, her treatment of Liir is one of Elphaba's biggest failures, and it's perhaps her inability to see this that is her biggest failing.