What does it mean to begin at the lower edge? (and the lower edge of what ?)
I would rather look at the pattern before i answer this...but....
It is my assumption that they are telling you that you are starting at the lower edge. Sometimes a pattern will tell you that ...so ill rewrite that instruction for you...
"leave a 40-inch tail of yarn for finishing. cast on 116 stitches to begin the lower edge of the cap"
Hope this helps