Cut shell of lobster tails lengthwise on the underside, using kitchen shears. Pry open tail segments; remove meat, reserving tails to use for garnish. Slice meat in 1/2-inch medallions. Cover and chill.
Sauté onion in hot canola oil in a large skillet over medium-high heat 10 to 15 minutes or until tender. Stir in brown sugar, rice vinegar, and orange juice. Cover and chill.
Pour vegetable oil to a depth of 2 inches into a Dutch oven; heat to 375°. Deep-fry spaghetti, a few strands at a time, for 10 seconds or until golden. Drain on paper towels.
Arrange lobster medallions, onion, papaya, lettuce, and fried spaghetti; drizzle with Sesame Miso Dressing. Garnish, if desired.
*Maui onions are from the Hawaiian island of the same name. Any sweet and mild onion can be substituted.