It turns out that a lot of people are allergic in various degree to the pollens contained within the flowers of many stripes. For some reason lilies are among the worst offenders, though if the stamina—plural of stamen—are removed apparently the pollen count is much reduced. Check this stuff out at Wikipedia.
The above display was just in front of the altar at St Patrick's Co-Cathedral this past Easter Sunday. And also see below. I almost forgot: cats can suffer from many problems from all parts of the lily plant, especially kidney failure.