Yes, it is a lily, I have two different unnamed Asiatic lilies with stems & leaves that look similar to that. They both have delicate slightly downturned flowers. I will post pics from last year, sorry about the quality but I had a bad camera last year and they have not bloomed yet this year.

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I may be way off base with my guess as to the flower form, but in any case it is a lily and should be in moist but well-drained soil (lily bulbs will rot if flooded), and full or nearly full sun.

Is that website your photography? I looked at a couple of the pics and they are beautiful!