I’m not exactly sure about the company/restaurant that you mentioned, however, I’m an independent consultant with The Pampered Chef® and we have a molten lava cake recipe that I think you could substitute with lemon and it would work.
It uses the Rice Cooker Plus by The Pampered Chef® and you mix the cake ingredients in the cooker, then put half of a can of ready made lemon frosting in the center. Cook in the microwave for 8-10 minutes or until cake tester comes out clean. Invert on plate (make sure that the plate has sides to it so that the lava won’t run off of the plate) and serve.
Hope this helps!