Step 1Make fresh pasta dough by pulsing flour and 2 teaspoons olive oil in food processor. Add egg and pulse until dough forms ball that rides around on top of blade. Remove from food processor and knead either by hand or on a pasta machine until smooth and shiny. Wrap in plastic wrap and refrigerate at least 1 hour.
Step 2Roll pasta dough out as thin as possible. Flour frequently. If using pasta machine, you will almost certainly need to dust with flour before rolling at narrowest setting. Sheets should be at least 4 inches wide (about 1 inch narrower than length of asparagus spears). Cut pasta sheets in 6-inch lengths, dust with flour and set aside until ready to use.
Step 3Snap bottoms off asparagus spears but do not peel. Place spears on in? jellyroll pan and lightly coat with olive oil. Salt to taste. Roast asparagus in oven at highest temperature until cooked through, 7 to 10 minutes. Shake occasionally to keep from sticking. When cooked, remove from oven, squeeze lemon juice over and set aside to keep warm.
Step 4Cook 4 or 5 pasta sheets at a time in plenty of rapidly boiling salted water. Pasta will be done when sheets float to surface, 1 to 2 minutes. Remove from boiling water and drain on tea towel if using immediately or transfer to large bowl of water to store. Repeat using all pasta.
Step 5(Dish can be prepared to this point at least 1 hour ahead of time. Asparagus should be cooled and stored tightly covered; cooked pasta sheets should be stored in large bowl of water and should be drained and patted dry before using.)
Step 6Combine pasta in mixing bowl with asparagus, butter and 2 tablespoons Parmigiano-Reggiano and toss to mix well. Divide among 4 pasta plates and return to 350-degree oven to heat through, about 5 minutes.
Step 7Pour any remaining butter in mixing bowl over pasta and dust lightly with remaining Parmigiano-Reggiano. Serve immediately.