Put the flour, salt and cayenne in a bowl, and mix well. Add the beer and stir until just incorporated. Mix no more than is necessary to prevent dissipation of the bubbles. Put at least 3 inches of canola oil in a deep fryer, and bring to 375 degrees F (or in a large heavy-bottomed saucepan, pour enough oil to fill the pan about a third of the way. Heat over medium heat until a deep-frying thermometer inserted in the oil reaches 375 degrees F.) Cut the haddock fillets into 3-inch pieces. Season the fish with sea salt and black pepper. When the oil is at temperature, (if you don't have a thermometer you can test it by dropping a bread crouton in. If it sizzles on hitting the oil, it's ready), dip the haddock pieces in the batter, and let the excess drain by holding it up briefly above the bowl before placing into the pan. Lay the fish into the hot oil slowly to make sure the oil hits all the surface area. Cook about 2 to 3 minutes on one side and flip over for another 2 minutes. You are looking for a golden brown color and crisp exterior. When ready, lift the fillets out with tongs and lay on paper towels, to absorb the excess surface oil. Open out the split baguette and place inside down in a large pan coated with a nub of butter, melted, on medium heat, for about a minute. This will pan grill the inside of the bread making it buttery and toasty. To assemble: Spread Tartar sauce on both sides of the bread, lay on two pieces of fish and add a final little crunch of some finely sliced iceberg lettuce.
Place 4 tablespoons of mayonnaise in a bowl and add all the ingredients. Mix together. Mixture should be green, chunky and not too runny.
Put the eggs and mustard in a food processor. While running the machine, slowly drizzle in the oil until it gets very thick. Add some water, and then continue with the oil. Shift back and forth between the oil and water. When all is added, add the lemon zest, lemon juice, salt, and pepper, to taste. Set aside.