It's Alstroemeria, also known as Peruvian Lily, but not a true lily (i.e., not a member of the genus Lilium).

They're not hardy in my zone 7 garden, so I can't pass on any experience with growing them. But, they do make great cut flowers and even the smallest buds will open if you change the water frequently and snip another half inch from the cut end of the stem every other day or so.

- Steve