I think the most important lesson Lyddie learns from Diana is that no matter how hard it is to get by in the world, it is both important and possible to retain one's humanity while achieving one's goals.
Diana, like Lyddie, faces tremendous odds in making it on her own. She says,
"I was orphaned young. I'm used to it. I suppose this mill is as much home as I can claim" (Ch.11).
Known as a radical because of her active support for the burgeoning labor movement, Diana never pressures others to adopt her ideas, and her strongest purpose in life is to make things better for the factory girls and people in general in whatever way she can.
When Lyddie first arrives in Lowell, it is Diana who gives her writing materials and urges to let her family know where she is, and when Lyddie is hurt in an accident in the factory, it is again Diana who helps her get medical attention. Diana teaches Lyddie to work the looms on her first days at work, and puts Lyddie to shame when she takes over Brigid's initiation, kindly showing the new girl the patience and reassurance Lyddie cannot give because she is so obsessed with making as much money as she can. Through her selflessness, Diana is a constant reminder to Lyddie of the importance of remaining human, and when she leaves, it appears that her influence has had a lasting effect.