Step 1In a blender or food processor, puree the cantaloupe until smooth. Set aside.
Step 2In a small saucepan, bring the sugar and 6 tablespoons water to a simmer, stirring, just until the sugar dissolves. Remove from the heat and let cool to room temperature. Add 2 to 3 teaspoons of the syrup to the cantaloupe puree, or more to taste, depending on the sweetness of the fruit. Add the lime juice to taste. Remove the puree to a small glass loaf dish and place in the freezer, stirring every 20 minutes to half an hour until frozen enough to shape into quenelles, 2 to 3 hours.
Step 1Cut the cucumber into about 1-inch chunks and process in a food processor or blender until pureed. Strain the puree through a cheesecloth-lined mesh strainer to extract the juice. You should end up with one-half cup juice. Discard the solids.
Step 2Soften the gelatin in a small bowl of cold water. Combine the cucumber juice and sugar in a small saucepan over medium-low heat until warmed, about 1 minute. Squeeze the gelatin sheet to drain and stir it into the cucumber mixture until dissolved. Stir in the lemon juice and season with a pinch of salt, or to taste.
Step 3Chill the mixture in the saucepan over a bowl of ice water, stirring occasionally, until the mixture just begins to thicken, about 15 to 20 minutes.
Step 4Oil the sides only of four (6-ounce) ramekins. Spoon the cucumber gelee evenly into the bottom of the four ramekins. Chill until almost set, about 2 hours.
Step 1Soak the gelatin in a bowl of cold water to soften. Meanwhile, warm the honey in a small heavy-bottomed saucepan over medium-low heat just until it thins out, 1 to 2 minutes. Squeeze the gelatin sheet to drain any excess moisture and stir it into the honey to dissolve. Stir in the yogurt until blended. Chill the pan in an ice bath until the mixture thickens and mounds slightly, about 30 minutes.
Step 2Carefully spoon the mixture evenly into the 4 (6-ounce) ramekins over the gelee layer. Chill until set, at least several hours and preferably overnight.
Step 1Slice the cucumber lengthwise into thin "noodle-like" strips, preferably using the julienne setting on a mandoline. Slice the cucumber on one side until you reach the seeds, then turn the cucumber and slice the second side down to the seeds. Discard the center of the cucumber with the seeds.
Step 2Dress the noodles with lemon, salt and sugar. Let stand about 15 minutes for the flavors to blend.
Step 3Divide the noodles among 4 serving plates, arranging each portion in a small mound on the plate. Unmold the panna cotta next to the noodles and top the noodles with a small quenelle of cantaloupe sorbet. Sprinkle a little chopped mint over the sorbet and serve immediately.