GitUp have said (on RCG) that a lens cap has been developed. It should be offered to early customers who do not have one. I'm not aware of a simple solution, although @Nigel did suggest something a while ago. I keep my F1 in the plastic bag in which it was shipped, inside a drawstring cloth bag.
On Dec 16th, @gitup wrote, "The future batch will include a lens cap by default, also we will offer some free lens cap for users who already bought F1 before."
If anyone has an original Xiaomi Yi lens cap, they could give it a try...
I think I worked out that was about the right size, but I don't have one to try.