Lyddie's sister Agnes died because of illness. Illness is part of the Man Vs. Nature category. On page (88) "Babby Agnes is gone to God."
Amelia and Betsy are arguing about signing the petition. This shows Man Vs. Man because they are fighting each other. On page (99) "I've made up my mind to sign the next petition. You wouldn't!"
Ezekial is a runaway slave who is trying to get to Canada. This is Man Vs. Society because the White people are hunting him. On page (42) it says, "It's a lot of money, he said gently." Ezekial knows that the White people are against him.