Heat oil in Dutch oven over medium heat until shimmering. Add onion and chorizo and cook until onion is softened and lightly browned, 5 to 7 minutes. Stir in garlic and saffron and cook until fragrant, about 30 seconds. Stir in clam juice, water, wine, potatoes, and bay leaf and bring to simmer. Reduce heat to medium-low, cover, and cook until potatoes are almost tender, about 10 minutes.
Pat hake dry with paper towels and season with salt and pepper. Nestle hake, skinned side down, into pot and spoon some broth over top. Bring to simmer, cover, and cook until potatoes are fully tender and hake flakes apart when gently prodded with paring knife and registers 140 degrees, 10 to 12 minutes.
Carefully transfer hake to individual shallow bowls. Using slotted spoon, divide potatoes and chorizo evenly among bowls. Discard bay leaf. Stir lemon juice into broth and season with salt and pepper to taste. Spoon broth over hake, sprinkle with parsley, and drizzle with extra oil. Serve.
