The irony in their relationship is how similar the two characters are to each other despite appearing very different at first. Lyddie is a girl, Ezekiel is man. Lyddie is a young teenager, Ezekiel is a mature adult. Lyddie is white, Ezekiel is black. Lyddie is not a slave, Ezekiel is a slave.
Of course Lyddie doesn't feel that she is a slave at first anyway. But after talking with Ezekiel, she realizes that they are similar in a lot of ways. Both of them have been forced to work in locations not of their choosing. Ezekiel is a plantation slave, but Lyddie is a slave in her own way too. She has been forced to take a job she does not like at the tavern in order to pay off her father's debts. They both long for freedom. Lyddie wants to be independent, especially financially independent. Ezekiel longs to be free from slavery. Both characters are proud and honest people. Both work tirelessly, and both characters share a love of learning. So while it would seem that they are nothing alike, the audience is privy to seeing exactly how much they are alike.