It belongs to the state, it was lent to Leopold and Lilian by the state, so after Lilian's death it went back.
But after Leopold died in 1983 Lilian sort of let it crumble down. She didn't want to touch anything anymore, and leave everything as it was when her husband died. Which was pretty stupid because now, 20 years later there's a lot to be repared and restaured. The costs have got so high, that the Belgian state doesn't want to pay it, and has decided to sell the estate.
(BTW it was built somewhere in the 1920's by a rich American).