Bring a large pot of water to a boil over medium heat. Salt the water, add the spaghetti and cook 1 minute shy of al dente. Remove a ladle of the pasta water and reserve. Drain the pasta and set aside.
Meanwhile, chop and reserve 1 lead lettuce. Chop second head and add to a food processor with the parsley, basil or tarragon, mint, pine nuts, lemon zest, salt and pepper, to taste, and the cheese. Pulse to chop the greens, then with the processor on stream in 1/4 to 1/3 cup of extra-virgin olive oil, to form a pesto. Transfer the pesto to large pasta serving bowl and reserve.
Heat 2 tablespoons extra-virgin olive oil in a skillet over medium heat. Add the leeks and garlic and saute until wilted, 3 minutes. Add the grape tomatoes, stir, raise heat a bit and put a lid on the pan. Cook for 8 to 10 minutes to burst tomatoes - force the last few along with a potato masher or a wooden spoon if you get impatient. Season with salt and pepper, to taste, then stir in the wine and cook for 1 minute.
Add the ladle of the reserved pasta water to the pesto. Add the pasta to the bowl along with the tomatoes and leeks. Toss for 1 minute, and season with salt and pepper, if needed. Douse the pasta the lemon juice and garnish with the reserved chopped lettuce. Serve with extra cheese for topping.