If it's not already clean, remove the fish scales (using either a fork, knife or fish scaler) and rinse well under cold water (the belly and neck tend to have the most scales).
Once the fish are thoroughly cleaned, cut each one into 2-3 parts (about 150 grams each part). Season the fish with kosher salt and freshly ground pepper. Set aside.
In a medium-sized pot, add the water, olive oil, and onions. Bring to a boil over high heat. Reduce heat to medium and boil for 30 minutes.
Add the carrots and celery and simmer for another 15 minutes. Season with salt and pepper.
Add the potatoes and cook them until they feel soft when you prick them.
Lay the fish parts on top of the potatoes. Bring the heat to medium-high and with the lid half covering the pot, cook the fish for about 15-20 minutes. Do not attempt to flip it because you'll probably destroy it.
Remove from heat and pour the fresh lemon juice on top. Shake the pot for the juice to spread evenly and you are ready to serve!