Cook and refrigerate the seafood up to one day in advance. Prepare the dressing, slice the fennel, tear the lettuce, and refrigerate separately. Assemble just before serving.
Combine wine and mussels in a Dutch oven over medium-high heat. Cover and cook for 5 minutes or until mussels open; discard any unopened shells. Remove mussels from pan with a slotted spoon, reserving liquid. Remove meat from mussels, and discard shells. Place mussels in a large bowl. Line a sieve with dampened cheesecloth, allowing cheesecloth to extend over edge of sieve. Drain cooking liquid through sieve over a bowl, reserving liquid; discard cheesecloth.
Return liquid to pan; bring to a boil. Add shrimp and squid to pan; cook for 4 minutes or until done, stirring occasionally. Remove shrimp and squid with a slotted spoon; discard liquid. Add shrimp and squid to mussels.
Combine 1/4 cup lemon juice and next 6 ingredients (through garlic) in a bowl, stirring well with a whisk. Drizzle lemon juice mixture over shrimp mixture, tossing to coat.
Combine lettuce and fennel in a large bowl. Add remaining 4 teaspoons lemon juice to fennel mixture, and toss to coat. Arrange fennel mixture on a platter; top with shrimp mixture.