If you don't want to opt for the lobster, this dish can be made with shrimp instead. About 20 oz of large raw shrimp. Just peel and devein the shrimp, then saute uncovered in butter until opaque in center, about three minutes. Cut each shrimp lengthwise in half.
Melt butter in heavy large skillet over medium-high heat. Add lobster tails and saute until shells are bright red in spots, about 5 minutes. Cover skillets;reduce heat to low and cook until lobster is cooked through,about 6 minutes. Remove from heat. Using slotted spoon,transfer lobster to work surface. Using heavy large knife,cut each tail lengthwise in half. Remove meat from shell. Cut meat crosswise into 1/2 inch pieces.
Return same skillet to medium-high heat(do not clean). Add mushrooms,half of basil,green onions,and garlic; saute until mushrooms soften,about 5 minutes. Add cream and clam juice. Boil until sauce is slightly thickened,stirring occasionally,about 10 minutes. Reduce heat to low. Add lobster(or shrimp if using) and simmer 1 minute. Stir in remaining basil. Season sauce to taste with salt and pepper.
Meanwhile,cook pasta in large pot of boiling salted water until tender but still firm to bite. Drain well. Return to pot. Pour sauce over pasta and add cheese;toss over low heat until warmed through, then serve.