Lyddie feels like a slave when she is sold to the tavern.

Lyddie is not actually a slave, but she sometimes feels like one.  Her mother sells her and her brother to pay off the family debts.  Since she has no choice in the matter, Lyddie feels like she is enslaved.

Working at Cutler’s Tavern feels like slavery to Lyddie because her mother forced her to leave the farm in order to work off the family's debts.

Once I walk in that gate, I ain't free anymore, she thought. No matter how handsome the house, once I enter I'm a servant girl‐no more than a black slave. She had been queen of the cabin and the straggly fields and sugar bush up there on the hill. But now someone else would call the tune. (Ch. 3)

Lyddie really does not like the tavern.  When she is given a new, storebought dress to replace her worn and outgrown one, she considers it symbolic of her bondage.  Lyddie blames her mother for sending her and her brother to work and breaking the family up.

When Lyddie meets an actual runaway slave, he recognizes her situation as a sort of slavery.  Even though she often thinks of herself as a slave, she gets defensive about the situation when talking to a real slave. 

"I couldn't leave my home," she said.

"No? And yet you did."

"I had no choice," she said hotly. "I was made to."

"So many slaves," he said softly.

"I ain't a slave," she said. "I just‐I just‐‐" Just what? "There was the debt my father left, so . . ." (Ch. 6)

Lyddie’s insistence that she will not be a slave extends to her factory life.  She is more concerned with making money to free herself from bondage than anything else.  When the girls compare factory life to slavery in an old song, Lyddie insists that she is better off now.

"I ain't a slave!" said Lyddie fiercely. "I ain't a slave."

"Of course you aren't." Amelia's confidence had returned and with it herschoolmarm manner.

"At the inn I worked sometimes fifteen, sixteen hours a day and theypaid my mother fifty cents a week, if they remembered. Here‐" (Ch. 12)

Lyddie takes the old song personally.  She feels that working in the factory she is in charge of her own destiny, where at the tavern she was not.  She does not want to think that she escaped one kind of slavery to enter another.  However, the factory life is very restrictive.  The girls work long hours and have few rights. 

"I ain't a slave" is a mantra that Lyddie repeats to remind herself that she could always leave, but she feels enslaved to the family debt.  Until she gets that money, she will never be actually free and her family will remain apart.