Prepare the vinaigrette, just before use. Place the lime in a small microwave-safe bowl and microwave until the essential oils in the skin are released. Since the lime will be hot coming from the microwave, you will need to set it aside briefly, until it cools just enough to handle. Pour vinegar into a blender, turn it on, and then squeeze in lime juice from the micro-waved lime. Leaving the blender running, add 1 at a time through the feed opening: mint, mustard, garlic chives, honey, salt, and ground pepper, and blend until smooth. While keeping the blender running, add oil through the feed opening in a slow stream.
Heat grill. Brush fennel and mushrooms with olive oil, and season with salt and pepper. Grill until they begin to soften, and then allow cooling.
Bring a pot of water to boiling. Have a bowl of ice water standing by. Add salt and blanch green beans for 2 to 3 minutes, then stop the cooking by plunging into the ice water.
Separate the lettuce into bite size pieces and add to a mixing bowl with oranges, cucumbers, and mint. Slice the fennel and mushrooms and add to the bowl. Add dressing and toss to coat.