Interesting that you'd heard these called Peruvian Lilies. I'd never heard that common name associated with this plant. I had a flower known as alstroemeria in my wedding bouquet (along with lilies, roses, and purple statice), and the florist referred to those as Peruvian Lilies.
I suppose the common names vary a lot from region to region. That is part of why I found this plant so interesting. It was really unusual looking, and also shared a common name with a very different plant I was already familiar with.