Add 12 cups of water to a large stockpot. Add salt and bring to a boil.
To make lemon tarragon drawn butter, melt the butter in a heavy saucepan over medium-low heat. When butter is fully melted, remove from heat and transfer to a glass measuring cup, or something similar. Let stand for 3 minutes. The butter should settle into 3 layers: a frothy top, a clear yellow middle, and a milky bottom. Begin by skimming or spooning the froth off the top. Then carefully and slowly pour out the clear middle layer into a bowl while retaining all of the white milky sediment in the cup. Discard the froth and white milky solids. If necessary, repeat the skimming process on the remaining butter in the cup.
In a small pot over medium-low heat, add clear butter, tarragon, lemon zest, and 2 tablespoons of lemon juice. Let simmer for 15 minutes. Strain off solids and transfer butter to a serving bowl.
Puree all the ginger mango puree ingredients in a blender or food processor until smooth.
To make aioli, add the garlic, egg yolk, lemon juice, salt, and pepper to a blender or food processor and puree until smooth. If you do not have a blender or food processor, whisk the ingredients together in a bowl. Slowly drizzle in oil with the motor running and puree until aioli thickens (should take 2 to 3 minutes). Cover and refrigerate. If you are using a whisk, keep beating while very gradually adding the oil until the aioli is thick¿this will take several minutes.
To make soy-wasabi sauce, put the wasabi in a bowl and add 2 tablespoons of the soy sauce.
Using the back of a spoon, blend until wasabi is dissolved. Add the remaining soy sauce.
Bring a large pot of salted water to a boil. Drop the live lobsters headfirst into the pot, cover tightly, and say 10 Hail Marys. Boil for 8 to 10 minutes per pound (12 minutes should be perfect for 1 1/4-pound lobsters). The lobsters will be a deep red color when done. To double-check doneness, pull off 1 of the walking legs. If it comes away easily, it is done.
Serve with dips.
Recommended beverage: White Burgundy
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.