Prepare the lemongrass by removing the outer tough leaves to reveal the white center. Smash each stalk with the back of a knife to release the oils and flavor.
Lay the sliced limes in the bottom of a large baking dish. Evenly space the lemongrass pieces on top of the limes and lay the ginger strips evenly around the lemongrass. Arrange the fillets directly on top, pour the sake over the fish and season with salt. Cover the dish with aluminum foil and bake until the fish is firm, opaque in the center, and beginning to flake, about 15 minutes. The cooking time varies depending on the thickness of the fillets.
Just before serving, spoon a little of the liquid from the dish over the fillets and transfer to plates to serve.
I used unfiltered sake to keep it even creamier, but any sake works. Mirin is a good substitute if sake is hard to find.