For the lobster and basil oil:
1) Combine oil and basil in a blender and blend for 2 minutes. Strain into a bowl and season with salt and pepper.
2) Preheat the griddle to high. Thread 2 skewers through the lobster tails lengthwise so that the meat will lie flat on the griddle. Brush the flesh with basil oil and season with salt and pepper. Griddle, flesh side down until slightly charred, about 2 to 3 minutes, flip over, brush top with more of the oil and continue to griddle until just cooked through, about 2 minutes longer. transfer to a serving platter and keep warm.
For the corn-coconut milk sauce:
1) Preheat griddle to high.
2) Remove corn from water, place on the griddle, close the cover and steam in the husk until tender, about 10 minutes.
3) Remove from the griddle, let cool slightly and remove the husks. Brush the corn with oil, season with salt and pepper and griddle until the kernels are slightly charred. Transfer to a cutting board and let cool slightly. Remove the kernels using a chef's knife and add to a bowl.
4) Heat about 1 tbsp of oil in a medium saucepan over a high heat. Add the onion and cook until soft. Add the garlic and cook for 30 seconds. Add the corn and toss into the mixture. Pour in the coconut milk, bring to a simmer and let cook for 5 minutes.
5) Allow the mixture to cool slightly; add to a food processor and puree. stir in the basil and season with salt and pepper, to taste. transfer to a serving bowl and serve with the lobster.