Bring a large pot of water to a boil for pasta. Cook pasta to al dente according to package, about 7-8 minutes. Slice asparagus in 1-inch pieces on an angle. Cut beans into thirds, also on an angle. Midway through cooking the pasta, add asparagus and beans to water so they cook 3-4 minutes in boiling water with the pasta. Add peas to the pot 1 minute before draining. Reserve about 1/2 cup starchy cooking water just before you drain the pasta.
Meanwhile, heat EVOO in pan and melt butter into it over low to medium-low heat. Add chives and garlic and stir a minute or two. Then add wine and gently reduce a couple of minutes more. Stir in Dijon and lemon juice and turn off heat. Add pasta and remaining starchy water and toss to coat evenly 1-2 minutes. Add some cheese and pepper to taste. Fold in baby lettuce and serve with extra cheese on top.