Meanwhile, in a mini processor, mince the ginger with the lemongrass. Heat 2 tablespoons of the oil in a medium skillet. Add the ginger and lemongrass and cook over moderately high until fragrant, about 2 minutes. Add the tomatoes and cook, stirring, for 1 minute. Add 2 tablespoons of the basil and the lemon juice and season with salt and pepper.