Luckstone (Magic Object, Trinket): Place 2 fate on this card. Whenever you pay a fate, you may discard 1 fate from the Luckstone instead. The Luckstone crumbles to the discard pile once both fate have been discarded.

May a character pay a fate from a Luckstone even if he himself doesn't have any?

It won't be very useful if you must have at least one fate remaining.

I think you may read it as "you may discard a fate token from the Luckstone instead of discarding it from your reserve", which doesn't imply that your reserve is not empty.

you can always use the fate off of luckstone, rather than your own stockpile.