BRUSSELS — To the long list of concessions that European monarchs have made to modernity, Belgium is adding another: submitting to a paternity test.

After refusing for months, King Albert II will soon give a DNA sample, his lawyer said this week, in a lawsuit brought by a woman who says she is his daughter, neglected and kept secret for decades.

But King Albert, who abdicated the Belgian throne in 2013, will still fight to conceal the result.

The paternity test could mark a dramatic turn in a lawsuit that has been underway for years, exposing Belgium’s secretive royal family to unusual public scrutiny and criticism.

There is more at stake than just recognition. The case could also make the plaintiff, Delphine Boël, 51, an heiress to the king’s fortune, which is estimated to be worth hundreds of millions of dollars.