Set a large pot of salted water to boil.
In a large skillet, cook bacon over medium heat, stirring occasionally, until crisp, 8 to 10 minutes. With a slotted spoon, transfer bacon to paper towels to drain. Pour off all but 3 tablespoons fat from skillet. Add the leeks, season lightly with salt to taste, and cook over low heat, stirring occasionally, until leeks are soft and beginning to brown at the edges, about 10 minutes.
Add pasta to pot and cook al dente. Reserve 1 to 2 cups of the pasta cooking liquid. In a medium bowl, whisk together eggs, parmesan, lemon zest, and lemon juice. Whisk 1/4 cup pasta water into egg mixture.
Add the pasta to the skillet with the leeks and immediately add the egg mixture, along with the bacon, and parsley. Season with salt and pepper to taste and add more pasta cooking as needed. Serve immediately with more parmesan and pepper on the side.