Lydia is pretty awesome. The game is post-Rebellion, actually, around 15 years after the movies, so there are still leftover messes to clean up. Lydia got caught in a slave ring that was kidnapping Force-sensitive kids and trading them to certain interests. She was resourceful enough to escape, but she lost her parents and was taken in by an old Jedi who'd hidden out from the Empire. He started training her, but he died before long, and Lydia inherited a small batch of orphans he'd been protecting.
Which is how the crew came across her. They tracked the slave ring to this planet, where they encountered Lydia and the other kids when she stole their credit chips to buy food. Most of the children were returned to their homes, but they were never able to find Lydia's parents, so she went back to the Jedi instead.
Now she's learning to be a Jedi healer, but she's still a sneaky, underhanded child with a wary streak and a smart mouth. She's saved their bacon a couple of times by not trusting random NPCs they took up with, but the great thing about her is that despite everything, she *is* a child, and while she's very competent (and distressingly world-wise), sometimes she acts her age.