How do Lyddie's actions affect other people in the story?

That's an interesting question.  I often think of Lyddie only helping herself or doing things that will help her earn money in order to pay off her family debt; however, that just isn't true.  Lyddie is constantly helping people despite her single minded focus of pursuing money.  
Lyddie's actions in the very beginning of the story save the lives of her entire family.  They are all sitting together in their home when a bear comes in.  Lyddie springs into action and bravely stands up to the bear, and the bear leaves.  
While returning home from Cutler's Tavern, Lyddie comes across Ezekial, a runaway slave.  She gives him her earnings, which help him to escape to free territories.  
Lyddie once again springs into action during the coach ride to the city.  The coach is loaded with men that can't get the coach out of the mud.  It is Lyddie who gets herself dirty and gets the coach unstuck.  
Lyddie is also the person that fends off Mr. Marsden's sexual advances from Brigid.  
I would say that Lyddie's actions throughout the story end up benefiting and protecting many other characters.