I almost had something similar happen to me so I could see how this happened. I prepaid for a scarf and went in 2-3 weeks later to pick it up. When I walked into the store my regular SA was on a break and not physically in the store. Since I was in a rush, another SA, trying to be helpful said my SA had told him i might come by, and that he knew which package it was. He came out with a wrapped up box in a large bag, and he didn't ask for ID or anything, nor did he check anything else... he simply handed me a bag. I grabbed it and was walking through the rest of SAKS when I remembered something else and went back into LV.
While asking about another item, I opened the box they gave me to put on the new scarf (I jut couldn't wait), and low and behold... there was something else in there. I was the one who pointed out to the SA that he had handed me the wrong box, as he did not realize the error. Turns out there were two boxes in the back and he obviously didnt know which box belonged to which customer. It kinda scared me that even after identifying that this was the wrong box, the SA still didnt put two and two together and I had to say to him - THIS ISN'T MINE! I was really glad I had discovered the error in the store as I would have been irritated if I had had to return to the store for this issue.
Just call up LV, I bet you the other customer already has. The SAs will eventually figure out who has the bag. It will all work out just fine!