Line 2 baking trays with parchment paper. Put the halved potatoes in a bowl with 2 tablespoons of the oil and toss to coat. Add salt and pepper to taste and toss again.
Spread out the potatoes on one of the baking trays. Bake for 30 minutes or until tender and browned at the edges, turning them over halfway through.
Brush the fish fillets on both sides with the remaining 2 tablespoons of oil and sprinkle both sides evenly with salt and pepper. Transfer to the other baking tray and bake for 10 minutes or until the fish flakes easily.
Carefully transfer the cod to the potato tray and add the green beans, garlic, and lemon juice. Drizzle with a little olive oil.
Transfer back to the oven and bake for an additional 10 minutes.