Preheat the oven to 450 degrees F. Heat 3 tablespoons of the olive oil in a large ovenproof pan until almost smoking. Season the chickens with salt and pepper to taste, place in the pan and brown all sides. Degrease the pan and place in the oven and roast the chickens until cooked through, 25 to 30 minutes. Let rest 15 minutes, then cut into quarters.
Bring a large pot of salted water to a boil. Add the lobsters and cover the pot. Bring the water back to the boil, reduce the heat, and continue cooking for 12 to 15 minutes or until cooked through. Cook the chorizo in a medium saute pan over medium-high heat until browned. Remove the chorizo to a plate lined with paper towels. Heat 2 tablespoons of the olive oil in a large saute pan or paella pan until almost smoking. Season the shrimp with salt and pepper and saute for 1 minute.
Season the squid with salt and pepper to taste and add to the pan. Continue cooking an additional 2 to 3 minutes until just cooked though. Add the rice, stock, peas, tomatoes, chicken, lobsters and chorizo and stir to combine. Add the mussels and clams, cover the pot and continue cooking until the clams and mussels open. Fold in the parsley and lemon aioli and mix until combined, season with salt and pepper to taste. Serve immediately.