Ummm google presents https://thewoksoflife.com/shrimp-lobster-sauce/ https://www.food.com/recipe/chinese-lobster-sauce-323257 https://rasamalaysia.com/shrimp-with-lobster-sauce/
No lobster involved - like fish fragrant eggplant - no fish. But since you have lobster stock and lovely new potatoes - I say experiment to your own taste.
From Fuchsia Dunlop They call this complex flavor “fish-fragrant” because it draws on the seasonings used in Sichuanese fish cooking, so it is supposed to recall to those who eat it the taste of fish.