Rinse the chicken pieces and pat them dry. Mix the oregano and paprika with some salt and pepper in a small bowl. Rub the spice mixture all over the pieces of chicken; marinate for 30 minutes so the flavor can sink in a bit.
Heat the olive oil in a paella pan or wide shallow skillet over medium-high heat. Place the chicken in the pan, skin-side down and brown on all sides, turning with tongs. Add the chorizo and continue to cook until the oil is a vibrant red color. Remove the chicken and sausage to a platter lined with paper towels.
Return the pan to the stove and lower the heat to medium. Make a sofrito by sauteing the garlic, onion, and tomatoes; cook until the mixture caramelizes a bit and the flavors meld; season with salt and pepper. Fold in the rice, stirring to coat the grains. Stir the saffron into the rice. Pour in the water and simmer for 10 minutes, gently moving the pan around so the rice cooks evenly and absorbs the liquid. Do not cover or constantly stir like risotto.
Add the shrimp, lobster, clams, the reserved chicken, and the chorizo. Give the paella a couple of good stirs to tuck in all the pieces and just let it simmer, without stirring, until the rice is al dente, about 15 minutes. Scatter the peas on top and continue to cook for 5 minutes, until the paella looks fluffy and moist. The ideal paella has a toasted rice bottom called socarrat. Allow to rest, off the heat for 5 minutes, and garnish with parsley. Serve with lemon wedges.