HEAT a pot over medium. Add oil, then shallots and garlic. Cook until shallots start to soften, about 3 min. Add peppers, tomatoes, paprika and wine, and cook 2 more min. Add sugar and salt. Season with fresh pepper. Bring to a boil, then reduce heat to medium-low.
ADD shrimp, mussels and lobster to tomato mixture. Cover and cook until shrimp have turned pink and mussels have opened, about 5 min. Discard any mussels that do not open. Top with basil.