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From my experience only stabbing weapons benefit from how far away they are used. (as in knives can 1 hit point blank.) I don't know of any weapon that can randomly 1 hit kill.
The lucky trait AFAIK only has an impact on your chances of repairing weapons, and possibly on loot tables too.
Lets say a baseball bat does 10 damage, and the average zombie has 30 health.
While you are not exhausted, you get a bonus of 50% more damage, bringing you to 15 damage per swing, from their, hitting a zombie at the sweet spot grants double damage, double 15 is 30, so under optimal conditions that ten damage baseball bat can deal way more damage then it should normally acomplish.
and this isnt even factoring increasing your skill with blunt, which for the sake of simplicity, lets just say 20% more damage per level, a person with level 5 blunt could hit for 60 damage while not tired and hitting the sweet spot, 30 damage while not tired and missing the sweet spot, 40 damage while tired yet hitting the sweet spot and 20 damage while tired and missing it.
A lot of factors determine just how powerful a melee weapon can be, and RNG does seem to play a role in the damage calculation, so this isnt exactly all correct, but essentially the best way to kill a zombie is to not be tired, and aim to hit it with the tip of the weapon, which is the sweet-spot zone.
Oh, and if it can be, use it with two hands for maximum efficiency, i have no idea if this increases damage or just makes the weapon less likely to degrade when striking or whatever, but whenever its an option for that weapon, always equip it with both hands.