The legal dispute stems from the terms of the former couple's divorce in 2009, after 16 years of marriage.
According to their divorce settlement, the 53-year-old reality star was given the family's mansion in Bridgehampton, New York. Alexandre alleges that the stipulation on that agreement was that Luann was supposed to set up a trust, benefitting their two children, using half of the interest of the estate.
Luann's ex-husband alleges in court documents, obtained by ET, that she failed to establish the agreed-upon trust. Instead, he claims she sold the mansion for $8 million, and used the money to buy herself a $3.1 million home in Sag Harbor, New York.
The suit alleges that, according to the conditions in their divorce settlement, Luann was allowed to sell their "marital residence," and reinvest that money in another house, so long as their children remained owners, in the form of their trust, of one-half interest in the new property.
Additionally, if the marital residence was sold more than the price of the new property, half of the profits from the sale would have to be entered into the trust. The lawsuit claims neither of these conditions were met.
Luann de Lesseps Explains How 'RHONY' Will Handle Her Arrest 'Drama' (Exclusive)
The court documents further claim that Luann "now threatens to list, sell or mortgage" the Sag Harbor property to buy a new home in upstate New York, without providing any money to the trust, which she allegedly has yet to form.
Alexandre, Noel and Victoria have therefore asked the court to block Luann from selling off the Sag Harbor home, and to order her to adhere to their original divorce agreement, which would include setting up the trust, and making giving them a half-interest in the estate.