Lilies are naughty flowers. That's why we love them so much.
Phototropism is just the habit of above-ground plant growth to reach for the light. The stems of some varieties develop more of a phototropic lean than others. I've never really thought about the stigma also being positioned for maximum light exposure before, but now that I think about the weirdly bent pistils on downward facing lily flowers from stems that have developed a great lean... the pictures in my memory all seem to suggest it was to get the stigma up toward the light via the shortest possible route.
Now I have imagery in my head of lily stems covered in pretty flower-faces all with an eye in the centre on the end of pistil-stalks!