Preheat oven to 400 degrees F (200 degrees C).
Grease a 9x13-inch metal baking dish with about 1 - 1 1/2 teaspoon olive oil.
Put the chopped tomatoes, aubergine, and carrot on the greased dish.
Place trout in the prepared baking dish and coat with remaining olive oil.
Season the inside and outside of fish with dill, thyme, and salt.
Stuff each fish with onion slices; grind pepper over the top.
Place 1/2 to 1 slice of lemon per trout.
Bake in the preheated oven for 10 minutes; add water to dish.
Bake until the flesh flakes easily off the trout with a fork, about 10 minutes more.