Preparation

Cook the seafood:

• Scrub the mussels well under running water and pull off any “beards.” Discard any mussels that don’t close tightly when tapped on the counter. Put closed mussels in a medium saucepan. Add about 1/2 cup water, just enough to cover the bottom of the pan by about 1/4 inch. Cover and set over high heat. Bring to a rolling boil and cook until the shells have opened, 1 to 2 minutes. Remove from the heat, transfer to a plate, and let stand until cool enough to handle. Discard any unopened ones. Remove the cooked mussels from their shells and put in a medium bowl; discard the shells and cooking liquid.
• To cook the remaining seafood, bring a 3-qt. saucepan of water to a rolling boil over high heat. Add the salt and let the water return to a boil. Pour the shrimp into the boiling water and cook until the largest one is pink on the outside, opaque on the inside, and just cooked through, about 2 minutes. The water may not return to the boil before they are done. Scoop them out with a slotted spoon and drop into the bowl with the mussels.
• After the water returns to a rolling boil, add the squid and cook just until they become firm and the rings turn bright white, about 1 minute. Scoop them out and drop them into the bowl along with the shrimp and mussels.

  When the water returns to a rolling boil, cook the scallops until just cooked through and no longer translucent inside, 1 to 2 minutes for bay scallops, 2 to 3 minutes for sea scallops. Scoop them out and drop into the bowl as well (if using sea scallops, you may want to halve or quarter them first).

  Add the lump crabmeat chunks to the bowl of seafood. Set the seafood aside on the counter while you prepare the dressing and other ingredients for the salad.

Make the dressing:

• In a medium-large bowl, combine the lime juice, fish sauce, sugar, chiles, and garlic. Stir to dissolve the sugar and combine everything well. Set aside.

Assemble the salad:

• Arrange the lettuce on a large serving platter or on individual serving plates as a bed for the seafood.
• Transfer the cooked seafood to the bowl containing the lime-juice dressing. Add the shallots and use your hands or a wooden spoon to gently toss everything well. Add the scallions, cilantro, and mint and mix well again. Scoop the seafood onto the platter or serving plates with a slotted spoon. Toss the cucumber and tomato in the dressing remaining in the bowl and scatter around the seafood. Drizzle any remaining dressing from the bowl over the salad, especially over any lettuce not covered by the seafood. Serve immediately.

Make Ahead Tips

The seafood can be cooked up to 4 hours ahead and refrigerated, covered. Let it sit at room temperature for 20 to 30 minutes before dressing.