Very Fancy Doilies was Lot #50 of the In Auction in The Ersatz Elevator. Before the auction, Duncan and Isadora Quagmire told the Baudelaire orphans that Count Olaf (disguised as Gunther) would hide them in one of the lots. Klaus Baudelaire researched the auction's catalog and guessed that Lot #50, titled "V.F.D." without any information about it, was the lot in question.
At the In Auction, Mr. Poe tries to bid on #48, an innocent-looking statue of a red herring. However, it is bought by the doorman. Gunther then skips to Lot #50, V.F.D., which appears as a cardboard box. The Baudelaires, with the help of Jerome Squalor, try to bid it, but are beaten by a man in sunglasses. Finally, at the last moment, Sunny shouts "Thousand!" and wins V.F.D. The Baudelaires tear open the box (wthout paying) but discover Very Fancy Doilies, not the two Quagmire triplets.
It turned out that the Quagmires were hidden in #48, the red herring statue. As part of Olaf's plan, the doorman, the hook-handed man in disguise, bought the herring. Olaf deliberately hid the meaning of V.F.D. in the catalog, writing it like so instead of Very Fancy Doilies, in order to fool the Baudelaires.
Once again, Olaf escapes, and the story goes on to The Vile Village.