This is a cucumber version of croûtes made with bread. This Provençal preparation is quite nice because the rich taste of lobster is suited to the light, watery cucumber.
Bring a large pot filled with an inch of water to the boil and cook the lobster until bright red, about 15 minutes. Drain, let cool, crack all the shells, and remove the meat and any tomalley and coral. Once the lobster is cool, chop and mix it with the mayonnaise and salt, pepper, and paprika to taste.
With a melon baller, scoop out the center of the cucumber