What is the gist of chapter 3 in Lyddie by Katherine Paterson?

By "gist" I believe that you are asking for a short summary of chapter three.

In chapter three, Lyddie has just arrived at Cutler's Tavern. Lyddie is to be a new serving girl at the tavern. Lyddie's mother sold her off in order to help pay off some family debt.

Lyddie is worked extremely hard by Mrs. Cutler. Lyddie never gives up, though, and proves herself to be a strong worker. Emotionally, Lyddie is miserable. The only comfort that she has comes late at night when she is able to count the money that she received from the sale of the calf.

There is a bit of foreshadowing in this chapter as well. Lyddie encounters an elegant woman who got off of the stagecoach. Lyddie is impressed by her presence and will learn (months later) that the woman is a factory girl who earns way more money than Lyddie is currently earning.