Start by combing your rice and lobster stock (or water) in a rice cooker (or cook according to package directions).
Once rice is cooked, remove from heat and let cool. Spread evenly onto a baking sheet and place in fridge to chill fully (at least 30 minutes).
Pick the meat from 2 cooked lobsters to remove claw, knuckle, and tail meat. Chop into small pieces and refrigerate until ready to cook. Reserve 1-2 tbsp lobster roe (the waxy red substance in the body) to mix with your eggs.
Prepare scallions by chopping into a thick dice. Place in a bowl until ready to cook.
In another bowl, combine soy sauces, vinegar, sesame oil, chili sauce, and oyster sauce and whisk until combined. Set aside.
Next, heat a large wok over medium-high heat and season with a thin layer of oil. Then, add 1 tbsp vegetable oil and heat.
In the meantime, crack and blend your 5 eggs with lobster roe (about 2 tbsp) until cohesive and orange-colored. Pour into hot oil and stir constantly with a wooden or metal spoon, scraping the wok to keep eggs from sticking.
Once eggs are fully scrambled and no liquid remains, transfer egg to a paper plate or baking sheet to cool and carefully wipe remnants of egg from wok. Re-season with a little oil.
Next, add your another 1 tbsp of vegetable oil to your wok and turn heat down to low. Meanwhile, chop garlic and ginger into a fine dice and add to your hot oil.
Stir constantly, for about 1-2 minutes, until garlic and ginger begins to brown. Remove from heat if it begins to burn. Then, add your chilled rice and stir.
Turn heat back up to medium-high and cook for 5 minutes, pushing rice to cover the wok in a thin layer. Then, add your eggs, most of the chopped scallions, lobster, and basil on top of the rice.
Stir the mixture together, scraping any stuck rice from the sides. Then, add your prepared sauce mixture and stir to coat all of your rice grains.
Cook for another few minutes to warm the rice and lobster completely. Then, turn off heat and serve immediately, garnishing with the rest of the scallions.