Keeping in mind that daylilies look different in different soils, climates, etc. etc....
...I have to say that no, it doesn't look like mine.
In my garden, CP is a pale pink, and it almost looks like a bitone to me. My plant gets quite a bit of shade, and I can't say that I ever noticed any lavender cast to it.
I apologize for the absolutely horrible images below
, but they were taken on different days this summer, and you can see that it is pink and the sepals are lighter than the petals. (The pink in these images actually looks darker than how I perceive the bloom in the garden; it normally looks pretty washed out to me.)
Also for comparison, from the database (and this is about what CP looks like, colorwise, to me - not like my images above):
You will notice that in all of these images, there are somewhat white-ish midribs on the bloom. Normally this is a trait that I loathe and despise - at least on darker daylilies - but the pink is (normally) so washed out on CP that there is not that much of a contrast (so it does not bother me that much).
I have to ask about plant traits.... does your plant seem as though it matches all of the registered traits for CP?
Something about your images brought the diploid 'Lavender Dew' (which I have) to mind. The color there can be somewhat variable. Tet 'Lavender Dew' was used in the generation of 'Lavender Memories', a Stamile plant, and your later images say Stamile to me. Perhaps that is the plant that you have - or maybe another Stamile lavender?