Microwave limes for about 30 seconds to release essential oils, and set aside to cool.
Turn on the blender and through the feed-tube, add the parsley, chives, honey, rice wine vinegar, and fresh ginger, and blend together until a smooth paste has formed. At this point the limes should be cool enough to squeeze. With the power on, add the lime juice through the blender feed-tube, and then very slowly add the oil and water until the mixture thickens and can coat the back of a spoon. Adjust the seasoning with salt and pepper. Set aside in refrigerator until needed. (When chilled, the dressing should resemble something like mayonnaise.)
In a large bowl, toss lettuce, tomatoes, cucumbers, and grapefruit with enough dressing to coat.