In the book Lyddie, what does Diana want Lyddie to do? Explain the movement. Explain Lyddie's feelings about participating.

I think the movement that you are referring to is the movement toward demanding better working conditions in the factories.  The girls are worked hard. Long days, few breaks, noise that can cause deafness, fibers in the air that cause lung issues, etc.  Some of the girls even start to compare themselves to slaves.  Diana wants Lyddie to publicly be a part of this movement for better working conditions by signing the petition that is circulating; however, Lyddie does not want to sign the petition.  Lyddie thrives on the tough working environment, and consequently is making really good money.  If she were to sign the petition, Lyddie risks being black listed from the factories completely.  If that were to happen to Lyddie, she wouldn't be able to get hired anywhere.  No work means no paycheck, and Lyddie desperately needs that money to get her family out of the financial debt that they are in.