It may sound corny, but friendship is like a bright light that can illuminate even the darkest times. Unless you're in The City of Ember, in which case a total power failure leaves everyone stranded in a pitch-black city unable to see a stinkin' thing, friendship or no. But we imagine it's still nice to have friends in those cases. Lina in particular learns a lot about friendship during her time in Ember: she learns about true friends and false friends, which friends have her back and which only care for themselves. There are as many kinds of friends as there are colors in the rainbow—which is to say, a lot.
Lizzie is a perfect example of a fair-weather friend. She's there when it's convenient for her, but when the going gets tough, she just gets going.
A good friend is never selfish, which is why Lina is the best friend of them all. She's only selfish once in the book.