This is a respectable tavern, Not the township poor house
Person vs Self
It's a lot of money
Lyddies whole family is at the cabin waiting for their porridge to cook when all of sudden a bear comes storming in their cabin due to the smell of the porridge. The bear somehow manages to get the pot of porridge onto its head. This is person vs nature because Lyddie is fighting the bear and the bear is part of nature.
Lyddie had just arrived at Cutler's tavern when she saw a stagecoach coming right at her when she met a woman who looked at her like she was a stray dog which Lyddie had not liked and had gotten mad for. This shows Person vs Person because Lyddie and Ms. Cutler don't like each other.
Lyddie is having a chat with Ezekiel when all of sudden he brings up the prize money for turning in a slave which he was and he would be tempted to turn him in if he were her. This shows Person vs. Self because Lyddie would be debating whether she should turn in Ezekiel for their money or should she not and make friends with him.