Two men come to the inn. What do Lyddie and Triphena overhear them talking about?

The answer to your question can be found in chapter four of Lyddie.  Lyddie is struggling with the workload being piled upon her at the inn, but her hard work and determination have earned her the respect of Triphena.  Triphena tells Lyddie the story of a frog that fell into a pail of milk and kicked and kicked so much that it churned some of the milk into butter and climbed on top to avoid drowning.  Lyddie is a "kicker" according to Triphena.  

Toward the end of the chapter, Lyddie is continuing her hard work around the customers, and she overhears a pair of men talking about slavery and slaves.  She hears them mention that there is money to make in the finding and returning of runaway slaves.  The conversation foreshadows Lyddie's coming encounter with Ezekial Abernathy, a runaway slave.