Check the dipstick.
An average car has say 4.5L of oil in it, and its normally 1L from min to max on dipstick. On the min whilst not great isn't likely to seize an engine in a short trip to the shops, but with no oil on the dipstick have you got 3.5L or 0L of oil??, 0L will ruin your engine in well under 1 mile, in fact with no oil will cause some engine damage in a couple of seconds.
If it was me and I had some oil on the dipstick I would run it very gently to a shop, if that was my only option for getting oil, no oil on the dipstick and i'd walk/taxi/phone a friend.
So far as it loosing oil, how much is it leaking/burning?,