Hi
As far as I know :
If you mean Reward Cloth White - obviously the answer is yes!
If you mean Dread Spider Silk White - the answer is only if you have any of that cloth left!
I don't think there is any way to do it with luna white dye (or other dyes) as you can with special wood deeds etc.
As for you wanting some - let us know how many you need and I'll see if Polly can make ye some!