If I have:

Apple Lemon Orange
3 0 1

How do I get Excel to look through the row of data, find the minimum (or
specifically, I am looking for the one and only Zero that would be in the
data), and return the cell above it? In this case, the returned value I am
looking for would be Lemon.

Tried =offset(min(range),-1) but I am guessing Excel won't let me use a
formula for the Reference part of Offset.