In a 4- to 5-quart pan over high heat, bring about 2 quarts water to a boil. Add lobster; when boil resumes, reduce heat and simmer until meat is opaque but still moist-looking in center of thickest part (cut to test), about 10 minutes. Drain lobster, then immerse in ice water until cool to touch, about 5 minutes; drain again.
Meanwhile, cut pit and peel from mango and discard; cut fruit into small chunks. Cut cucumber lengthwise into thin slices; stack slices and cut stack lengthwise to make 3/8-inch-wide sticks.
With scissors, snip underside of lobster shell free from back shell and lift off. Pull out lobster tail; discard shell. If vein is present, pull out and discard. Coarsely chop meat and put into a bowl. Add mango, onion, and mint; mix gently.
Shape 2 rolls at a time: Immerse 1 rice paper round in a large bowl of hot tap water, lift out, drain briefly, and lay on a counter. Let stand until paper is soft and pliable, about 30 seconds. Repeat to moisten another rice paper round and lay on counter.
Working quickly, spoon about 1/12 of the filling down the center of each wrapper, leaving 1 inch of the wrapper bare at both ends. Lay 1/12 of the cucumber sticks parallel to the filling and mound 1/2 cup salad mix on top.
Fold the 1-inch ends of each wrapper over filling, then, holding filling in place with your fingers, roll wrapper snugly around it. Press wrapper edges to seal; if edges are too dry to stick, moisten with a little more hot water. Set each roll, seam down, on a platter and cover airtight with plastic wrap.
Repeat steps 4 through 6 to fill remaining rice paper wrappers (replace water in bowl as needed to keep hot).
If making rolls up to 3 hours ahead, chill. Uncover rolls and cut each in half diagonally; if desired, stand rolls upright, cut ends up. Dip into mint-lime sauce to eat.