It's a play on words. The "Little Black Dress" was a very simple Coco Chanel number from the '20s or '30s that has become standard to this day, a mainstay of every (thin) woman's wardrobe, and has been called the LBD.
Your character's dress was apparently similiarly simple, but red. It is interesting to note that she poured her voluptuous curves into it. Pity the LRD.