The ironic Quaker commentary
By calling the book The Quaker City, Lippard shows how far the city of Philadelphia had fallen in his eyes, having been started by the Quakers, a highly religious people with strict moral and ethical guidelines for behavior. Flash forward to Lippard's day, when powerful and wealthy people seemed above the law. The novel is believed to have been inspired by real court cases, one of which involved the rape of a teenage girl at gunpoint—the defendant was ruled not guilty by reason of insanity.
The irony of monks and hedonists
By likening the brothel in the novel to a group of monks in a monastery, Lippard underscores the undeniable injustice of the behavior of the upperclassmen in the brothel. Hedonism is when a person's ethical philosophy serves their pleasure first and foremost, and if any of Lippard's claims are true about these alleged events, then hedonism is obviously at play. This adds a dark, sinister element to the tone, and the novel could be described as sarcastic, even to the point of outright hatred.
The irony of legal injustice
Another related, and seriously unfortunate, irony is the problem of the legal system failing. By forming a jury of one's own peers, the citizens expect that no one under any circumstance slips by the justice system, just because of how many strings they can pull or how important they are. But in 1850's Antebellum Philadelphia, there were riots, and the lower class was saying that they were being abused by the wealthy and powerful. Finally, a few of those cases were brought to trial, and the defendants were found not guilty because of bogus 'insanity' pleas. This inspired the novel, so it's not surprising that legal injustice is at the center of story. The powerful shouldn't be above the law, but Lippard saw that unfortunately they were, in a way.
The irony of empathy in the "brotherly city"
The name The Quaker City might even be a reference to William Penn (of "Pennsylvania," or "Penn's Woods"), who gave the name Philadelphia to the city. The irony with that would be that since the original vision of the city was a utopian community, the kind of terrible crimes that are alleged to be going on among the upper class stand against the very foundation of their city.
Irony of power and vice
With great power comes great responsibility, and generally speaking, it seems that many people do not handle that responsibility well. This novel shows an ironic relationship between power, money and vice. By vice, we mean behavior that is generally regarded as evil or unbecoming by a particular society. In the novel, the wealthy and powerful seem inclined toward this vicious behavior, often at the expense of victims whom they use for their own pleasure.