BILL, BILL, I found the name!!!
Your flower is an Alstroemeria. These are great garden or cut flowers. They come in about a squillion colours.
Here's a link to many many pics of Alstromeria.
The one we have outside our apartment, in bloom now, is a species one: Alstroemeria psittacina. I'll try to post a pic of it tomorrow if i get a chance.