For the Gremolata Breadcrumbs: In a medium skillet, combine oil and breadcrumbs and cook over medium-low heat, stirring occasionally, until toasted and golden brown, 5 to 7 minutes. Add parsley and lemon zest, season lightly with salt, stir to combine, and continue to cook until parsley begins to sizzle and mixture is very fragrant of citrus, 30 seconds to 1 minute. Transfer breadcrumb mixture to small bowl and set aside until you are ready to serve.

For the Lobster Fra Diavolo: Set a cutting board inside a rimmed baking sheet (this will help contain the lobster juices). Using a heavy chef's knife, kill each lobster by pressing the tip of the knife in the indentation just behind and between the eyes. Press down firmly, then split head in half.

Using kitchen towels, twist off tail and claws (including knuckles) from each lobster carapace. Remove and discard rubber bands from claws.

Roughly chop lobster bodies, reserving juices.

In a large pot, combine 1 cup (235ml) olive oil with the chopped lobster bodies and set over medium-low heat and cook, stirring and scraping occasionally, for 20 minutes; raise heat to medium midway through cooking.

Increase heat to medium-high and add white wine, bring to a boil, and cook, scraping bottom of the pot, until raw alcohol smell has mostly cooked off and wine is reduced by about half, about 3 minutes. Add 4 cups water plus any collected lobster juices and bring to a boil over high heat.

Arrange claws in an even layer on top of shells (they should be just touching the liquid but not fully submerged in it). Cover pot tightly and cook for exactly 3 minutes. Using tongs, transfer claws back to rimmed baking sheet. Arrange tails on top of shells, cover pot, and cook for exactly 2 ½ minutes. Using tongs, transfer to baking sheet with the claws. Lower heat to maintain a simmer and continue cooking lobster stock for 30 minutes.

Meanwhile, when tails and claws are cool enough to handle, remove tail, claw, and knuckle meat from shells using kitchen shears, lobster crackers, and/or the back of a heavy cleaver to help crack shells. Transfer shells to the pot of lobster stock as you go along with any accumulated liquid in the rimmed baking sheet. Cut lobster meat into generous chunks and transfer to the refrigerator. After it has cooked for 30 minutes, strain lobster stock; you should have about 3 cups (if you have less than 3 cups, top up with water to equal 3 cups; if you have more, simmer in a small saucepan until reduced to 3 cups).

In a large Dutch oven, heat remaining ¼ cup (60ml) olive oil over medium-low heat with the garlic and red pepper flakes until the garlic begins showing just the first signs of color, about 3 minutes. Stir in tomato paste and cook for 1 minute.

Add crushed tomatoes along with the oregano. Add lobster stock, increase heat to bring to a simmer, and cook, adjusting heat to maintain a simmer and stirring occasionally, for 10 minutes. Season lightly with salt.

In a pot of lightly salted boiling water, cook spaghetti until about 4 minutes shy of al dente. Using tongs, transfer directly into tomato sauce and cook, stirring, until spaghetti is al dente and sauce has thickened around it.

Add butter and stir until melted and well incorporated. Season with salt, if needed. Remove from heat and add reserved lobster meat, stirring until warmed through.

Transfer spaghetti and sauce to a large serving platter or individual plates. Sprinkle gremolata breadcrumbs on top and serve.