If someone wins a lot of money in the lottery and is called “a lucky stiff,” it means we think of him as a hard-working, average person who got lucky.
But the original meaning of the word stiff described a failure, someone with as much chance of earning that much money on his or her own as a dead person, also called a stiff.
A lucky stiff then means that a person, the lottery winner, in this case, is unworthy and undeserving of monetary gain.