While Oscar was the protagonist in the third-person pov of the first chapter, and we followed him from adolescence through his going away to college, Diaz switches us to first person pov of Oscar's sister Lola without warning in the second chapter. But then, that's what chapters are for; to designate a change of time, place, or character.
We've already been introduced to Lola and we see her as basically a caring older sister, encouraging and teasing the nerdy Oscar in his relationships. At school she seemed to be considered cool and Oscar holds her in high regard. But with the switch to Lola, we see a very different home life for her and Oscar. Even while discounting some of the usual mother-daughter misunderstandings, Lola claims to be mentally and emotionally abused by her mother, something that we didn't get the feel of from Oscar's story.
This reminds me a bit of Matthew Sharpe's Jamestown, where we get several perspectives of the same events from the different characters. It's a nice element in writing that allows the reader to make a better assessment of the environment by balancing out the different viewpoints. It also allows the reader to get a better feel of the characters by how they present their versions.
What we see of Lola's character is grit and determination, rebellion and strength; a much stronger player than the nurturing older sister we've come to know.