In a food processor, blend 1 cucumber, half of the cantaloupe, and half of the honeydew melon. Pour into a large bowl. and set aside.
Blend the remaining cantaloupe, honeydew melon, and cucumber. Add shallots, yogurt, and sherry vinegar and blend. With food processor running, add olive oil in a slow steady stream to emulsify mixture.
Whisk emulsion into the bowl of the reserved fruit blend. Chill for 3 hours.
To serve: Place thinly sliced prosciutto in bowl, add 1/2 of a lobster tail with the meat from one claw and ladle of cold soup. Garnish with a drizzle of mint oil and add a few beet chips. [mint oil: blanch 2 handfuls of fresh mint and half a handful of spinach. Pat dry and blend in food processor with 1 cup olive oil. Chill mixture for 1 day. Strain through coffee filter before using.]