Neither sentence is natural. The tenses don't match for a start - 'We were lucky we didn't run out/short. . .'
If you run short of something (you haven't much left) you are close to running out of it (you have none left).
'I'm running out of petrol; I'll have to find a filling station soon.'
'I've run out of petrol; I'll have to call the RAC (a roadside rescue service).'