We don't really learn much about Lydia's character in Chapter 3. In fact, she is really only mentioned by name once in the whole chapter. But one thing we learn about both Lydia and Catherine, the two youngest sisters, is that they are both very, very young, perhaps too young to be out in society. Austen expresses their youth in the lines:
... and Catherine and Lydia had been fortunate enough to be never without partners, which was all that they had yet learnt to care for at a ball. (Ch. 3)
From the phrase "yet learnt to care for" we can tell that they are still very young and still have a great deal to learn. Other things that they may in time learn to care for at balls is the opportunity to socialize with friends, to fraternize with fellow man, critique society, and even find a prospective husband.
The phrase stating that they "had been fortunate enough to be never without partners" is also a bit revealing. We already learn earlier that there are not enough men present at the ball for every woman to have a partner during every dance. In fact, Elizabeth had been forced to "sit down for two dances" when Darcy gives his famous snub, rejecting Mr. Bingley's persuasion to ask Elizabeth to dance, saying of Elizabeth that "she is tolerable; but not handsome enough to tempt me" (Ch. 3). Hence, the fact that both Lydia and Catherine have managed to dance every dance may show that they might be a bit more forward than their other sisters, perhaps more forward than society would allow young women to be. In fact, we learn later that they are both atrocious flirts in danger of dishonoring their family. Thus, this one passage describing Lydia and Catherine at the ball foreshadows what more we learn about their character traits in the upcoming chapters, namely that they are young, silly, and dangerous flirts, with Lydia being the worst of all and Catherine eagerly following Lydia's lead.