Most of the time we normally associate the recurved flower form on downfacing lilies, but this form can also be found on upfacing and outfacing lilies. In some cases it does show the flower to a better advantage because more of the "petal" surface can be seen especially on the taller upfacing lilies. This form can be considered a bit unusual and perhaps not to everyones taste, but once in a while it does give a striking lily I think. A few examples.
Jim

Love the recurved flower form

I actually like the recurved flowers in any orientation. Those are pretty.

I am very attracted to the recruved forms, but the mass producers are not since most of the market is for cheap lily blooms for florists and that type doesn't travel well.

The recurved forms most definitely for garden beauty.