Doug, it is a pretty basket. I do not think it is Zanetti because the signature does not look like his and the basket does not look like anything that he has done. I googled "Licio Zanetti vase" and found many things he has made. They all looked very much like his style. I couldn't find any glass similar to yours, and the signatures were all the same -- Zanetti L or Zanetti Licio with the sweeping Z.
Licio Zanetti's name carries a premium in Europe, though less so in the USA. This might explain why the basket is signed. Now why it is dated, I don't know. I can't remember seeing any of his work that is dated.