How to Make It
Using a mortar and pestle, mash together lemon juice, garlic, saffron, and 1/4 teaspoon salt until smooth and combined.
Scrape mixture into a medium bowl; whisk in egg yolk. (Alternatively, using the flat side of a knife, mash garlic and 1/4 teaspoon salt on a cutting board to form a paste. Transfer to a medium bowl; whisk in lemon juice, saffron, and egg yolk.)
Slowly drizzle in olive oil, whisking constantly, until emulsified. Whisk in remaining 1/2 teaspoon salt; cover and refrigerate up to 1 day.
Stir together garlic, fennel seeds, red pepper, 2 tablespoons oil, 3/4 teaspoon salt, and 1/8 teaspoon black pepper in a large Dutch oven. Cook over medium, stirring occasionally, until garlic begins to sizzle, about 3 minutes. Stir in tomatoes, wine, and saffron, and bring to a simmer. Reduce heat to medium-low, and cook, stirring occasionally, until sauce is slightly reduced, 12 to 15 minutes. Stir in 1 teaspoon salt and 1/8 teaspoon black pepper. Transfer tomato mixture to a bowl. Wipe Dutch oven clean.
Place a damp paper towel on a work surface. Top with a rimmed baking sheet; line with another damp paper towel. Fit a cutting board inside baking sheet. Place 1 lobster on cutting board, and straighten tail. With the blade of a chef’s knife over the head, pierce lobster straight down through the midline of the carapace (where the head connects to the body) until knife tip reaches cutting board. Using a lever motion, cut lobster’s head in half. Rotate lobster 180 degrees, and cut lengthwise through the midline, through the body and tail, to separate lobster into 2 halves. Remove and discard stomach sac from head, intestinal tract, and tomalley. If desired, using back of knife, crack claws on inner side, and loosen shells. Remove and discard rubber bands, if necessary. Repeat procedure with remaining lobster.
Sprinkle cut sides of lobsters with 1/2 teaspoon salt and 1/4 teaspoon black pepper. Sprinkle snapper pieces with remaining 1 teaspoon salt and remaining 1/4 teaspoon black pepper. Heat 1 tablespoon oil in Dutch oven over medium. Add 2 lobster halves, cut sides down, making sure claws are in contact with bottom of Dutch oven. Cook until meat is lightly browned, about 2 minutes. Flip and cook until claws are bright red, 1 to 3 minutes. Remove from Dutch oven. Add 1 tablespoon oil to Dutch oven, and repeat with remaining 2 lobster halves. Remove from Dutch oven. Add remaining 1 tablespoon oil to Dutch oven. Place snapper pieces in Dutch oven, skin sides down. Top with lobster halves, shell sides down. Add clams and mussels. Pour tomato mixture over seafood. Bring to a simmer over medium. Reduce heat to medium-low, cover, and cook until clams and mussels open and lobster claws are cooked through, 10 to 12 minutes. Discard any clams and mussels that do not open.
Serve stew immediately on warm plates or a platter with toasted bread spread with aioli and, if desired, salad.