Not a silly question Kapp,
Here is the way I store all my extra lanyards, and believe me I have way too many extras. Passholder lanyards, Christmas lanyards, my cherished Arizona Jeff adventure lanyards, my first black lanyards, my DIS green lanyard etc....
I seperate the bottom velcro which makes the lanyard into a strip of ribbon.
Roll the lanyard starting with the part without the clip. Then wrap it with an elastic band and let is sit for a few days. When you unroll it the creases should be gone. It may have a tendency to curl from being rolled but this will hang out as soon as you start adorning it with pins. The weight of your lanyard card or whatever you decide to put on the clip should also pull the curl out.