Symbolism, Imagery, Allegory
As a rule of thumb in literature, locks imply a lack of control (or taking control), a power discrepancy, and imprisonment. On the flip side, a lack of locks represents something too—here we can think freedom, trust, and other things. For our purposes in Sold though, we're going to focus on where we can see locks (although if you're interested in locks, you might spend some time thinking about where they aren't in the book, too).
When Lakshmi is first taken to the small room at the brothel, she thinks of all the things the money she will earn will buy her family on the mountain as she hears "the girl lock the door behind her" (64.TenThousandRupees.20). Gulp. Right away we understand that while Lakshmi is dreaming of financial freedom, she's actively being confined against her wishes—and the lock quickly comes to mean something more than captivity to Lakshmi:
I have grown to dread one sound more than any other: the rasping of the key in the lock, which means that Mumtaz has arrived with strap and her taunts. (76.ACupofTea.1)
So in addition to being trapped, the lock incites fear in Lakshmi because it implies pain—both physically and emotionally.
After the raid Anita steals a lock to keep Lakshmi and her safe in future raids—if the two girls lock themselves in to a small cupboard, "then no one will be able to open the door" (149.AHidingPlace.8). In this context, the lock represents safety from those who would harm the girls—in this case, the police who come to take a girl away when Mumtaz fails to pay them off. We're curious: Do you see this as Anita taking control or giving up freedom?
Finally, when Lakshmi is trying to get Anita to go with her toward the American's voice in the last chapter, there's a world of meaning when Anita "lets go of my arm, closes the door between us, and I hear a sad and final sound: the lock sliding into place" (177.TheWordsHarishTaughtMe.20). Anita is too afraid of the uncertainty of freedom, and instead stays in a place that she understands. Is this actually a choice, though, considering the many lies about the outside world that Mumtaz circulates around Happiness House?