The letter that Lyddie receives from her mother in Chapter 12 is truly a tragic letter. In the letter, Lyddie learns that her little sister, Agnes, has died and that her mom is in need of more money to help the family. (One can only imagine how hard it was for a mother to write her daughter with news such as this and, further, ask that daughter for help.)
Lyddie's reaction to the letter (which is the source of your question) is that she works ever-harder to help her hurting family. As one of the Lowell Factory Girls, she seems to lose almost all sense of self, not even complaining as the machines are sped up so she has to work harder. These new, rougher working conditions take a toll on all the girls. Prudence is forced to leave the factory due to the fibers in her lungs causing a persistent cough. The three girls left (Lyddie, Amelia, and Betsy) fight about a petition they could sign to improve working conditions. Lyddie's reaction is a direct result of her mother's letter. Lyddie doesn't want to bother signing the petition because she is afraid signing it could stop the money coming in to help her family. Lyddie cannot take a chance of this happening.
My heart is heavy, she thought. It’s not just a saying. It is what is—heavy, a great stone lodged in my breast, pressing down my whole being. How can I even stand straight and look out upon the world? I am doubled over into myself and, for all the weight, find only emptiness.
In conclusion, Lyddie decides not to pay attention to the horrible working conditions of the Lowell Factories due to her persistence in helping her hurting family.