The romantic dessert seems a bit fancier than the US lava cakes as they're made with Belgian Couverture chocolate. They're baked/heated to order and are only available through February 18, 2018 for 350 yen each (~$3.25 US).
Molten lava cakes are normally sold by Domino's in Japan but in a round shape and called "Freshly Baked Fondant Chocolate."
Photo via Domino's Japan.