When LuAnn married Count Alexandre de Lesseps (the great-great-great grandson of Ferdinand de Lesseps, who built the Suez Canal and presented the Statue of Liberty to the United States) she gained the title Countess, and was "legally entitled to the privileges of peerage," meaning that she had a "life estate in her husband's dignity." She is not a peer in her own right, but simply "style" alone. Still, it's considered a legal title.
She loses her legal right to the "peerage style"— being Countess LuAnn de Lesseps — following divorce. However, with divorce having become more and more common in the last couple of centuries, a convention was developed that allows divorced wives to retain a "courtesy title," which means that her first name will be placed before the title, followed by her last name, e.g. LuAnn Countess de Lesseps. This helps distinguish divorced wives from a peer's subsequent wives. She's not required to be addressed that way, and can instead go by her given name, or simply LuAnn de Lesseps. Knowing how much she's come to identify with her husband's aristocracy, I think it's safe to say that LuAnn will opt for the courtesy title.
LuAnn is actually Alex's fourth wife, and it's unknown if he has children from his previous marriages. On the show she mentioned that the family heirlooms and jewelry will get passed on to her son, who will inherit her husband's title. Does this mean that LuAnn's jewelry will be taken when the divorce is final, since it belongs to the title, and not necessarily to her?
In her most recent blog post, she said that her mantra is "if you don't take care of yourself, nobody else will," which is why she's taking a few days off to go to a spa. Perhaps she'll take some time there to reflect on what she thought was the problem with women: that they're "too equal" with men.
Count 'Housewife' Couple Out [NY Post]
Courtesy Titles [Wikipedia]
Earlier: Countess LuAnn: "The Problem Today With Women Is That They're Too Equal With Men"
LuAnn's Insistence On Being Called "Countess" Is Not Very Civilized