Carol already mentioned Indian Giver, but I just wanted to say it is probably one of my best purples.
Last year I received Purple Tarantula and it was just gorgeous in my garden this year. I love the way the petals curl. It is over 4 feet tall and it did lean a little, but as you can see in the picture, it does get some shade, so I think it might have been reaching for the light.
Here are some others to look at:
Backscratcher is a great daylily
I did a quick search on the AHS database with these filters:
Color in Description: purple.
Description Keywords: purple self.
It came back with 587 results! Of course, there were all different shades of purple, but it was fun to look at them.