For the gnocchi:
Peel potatoes, cut into 3/4-inch chunks, boil until tender, drain and passed through a ricer. Place the potatoes on a work surface dusted with a little flour. Add the egg yolks, water and salt and pepper to taste and mix lightly by hand. Add all but 3 tablespoons of the flour a little at a time, kneading gently just until incorporated. The dough should be soft but not elastic.
On a work surface, form the mass into a log. Divide the log into smaller portions and using your hands, roll out into 1/2-inch-long pieces. Dust them well with flour. Hold a flour-dusted fork, concave side up, in one hand. With the other hand, push a piece of dough into the tines, making an indentation with your thumb. Then roll the dough off the tines, making a shape like a tiny bowl with ridges on the bottom. Flour the fork and repeat with rest of dough.
Remove lobster claws. Crack claws, and remove the meat. Cut lobsters in halves, rub with oil and grill on a hot grill for 8 minutes. Pull the meat from the shells and set aside.
Cook gnocchi in boiling water for 4 to 5 minutes. Drain.
For the sauce:
melt butter in a large skillet. Stir in walnuts and lemon strips and cook 5 minutes. Stir in the lobster meat and gnocchi and cook 2 minutes. Season with salt and pepper. Add lemon juice. Remove from heat and stir in the parmesan.
Divide among 4 plates. Sprinkle with parsley. Serve.