Just wanted to comment that my girl with the PhD in Cell Biology says the white buildup is dead skin cells. I don't currently have the white line of gunk but there was a time (back in the Aquaphor days I believe) that I did get it.
Now I will notice towards the end of the buildup cycle the line between inner and outer lips will be white directly after consuming alcohol or spicy, greasy food or soup. After a little while it becomes unnoticeable again.
Just so you know it's not going to happen forever, and you can limit its appearance in public.