Yes, the Whiz can be folded, but it cannot be kept in that condition for long periods.
So if you need to roll the lilyshield to a pen like shape, squeeze it into a bag or pocket during a short trip, then it will bounce back to its original shape quite happily.
However, if you want to fold it for longer than a few days, depending on the conditions, don’t be surprised if, when you release it, your Whiz cannot spring back to its perfect shape.