Why does Lyddie return to the tavern?

I believe that you are asking about the end of chapter 6.  

In chapter 5, Mrs. Cutler decided to take a trip to Boston in order to sell some of the maple sugar and visit her sister.  Triphena announces to Lyddie that if Mrs. Cutler can have some time away from the tavern, then Lyddie should too.  Lyddie decides to go home.  

Once she arrives at home, Lyddie discovers that a runaway slave named Ezekial is hiding out in her farm house.  The two of them talk, and Lyddie realizes that her life at the tavern is similar to slavery. Nonetheless, it is her job.  Lyddie returns to the tavern, because it is what she needs to do to pay off her family's debts.  

Unfortunately, Mrs. Cutler is already back at the tavern.  She fires Lyddie immediately.  Lyddie is not heartbroken, because now she is able to go to Lowell and become a factory girl.  

She felt more lighthearted than she had since the day Mrs. Peck brought the letter. . . "I'm going to be a factory girl, Triphena. . . I'm free.  She's set me free.  I can do anything I want. I can go to Lowell and make real money to pay off the debt so I can go home."