Hi I'm Ryan8Ross, and I'm a Silver 1 player who mains jungle. THIS IS NOT A GUIDE. I will not tell you how to play lucian in this guide, nor will I claim I am a good lucian player, or that this is the best build to use. However, this IS the maximum damage you can do with The Culling (as of 3.10) WITHOUT THE INCLUSION OF RUNES. More to the point, it answers the question, AS vs AD.
Note: If you think you have found a build that can do more damage, feel free to PM me, and I will update the guide.
Note: I have not included Mejai's Soulstealer or Sword of the Occult in any calculations, as they are not viable items in any league of legends game, in my opinion
About 'The Culling'
ACTIVE: Lucian starts firing shots in the target direction for 3 seconds, each shot dealing physical damage to the first enemy it hits. The amount of shots fired scales with his attack speed. The Culling is considered a channeled ability and it can be interrupted, but Lucian can move freely (including movement abilities) without interrupting it himself.
Reactivate The Culling to cancel the ability early.
The Culling deals quadruple damage to minions but not monsters.
We are only interested in the damage, which at level 18, is calculated by
(60 base damage + 25% bonus ad +10% ability power) x (17 + (bonus AS x 0.149))
which is simply: (damage per shot) x (amount of shots)
Firstly, why the bad items, are bad items.
Blade of the Ruined King while this provides some nice stats for The Culling, giving bonus attack speed and attack damage, the passive is not utilised when using The Culling, and the stats make it a a more mediocre version of the Zephyr
Sword of the Divine The culling uses the attack speed of lucian when it is used to decide how many shots are fired, Riot realised very early that if The Culling took advantage of SotD's unique active, you could reach max attack speed with just 1 or 2 items and it would be way too strong, so they made it explicit that this would not work when using SotD
Muramana Same as before, Riot have made it expliticly clear that each shot will not benefit from the muramana toggle, or it would almost double the damage you can do
Infinity Edge Since the shots cannot crit, an infinity edge would not give you as much damage as The Bloodthirster and therefore is just a worse option
After calculating the damage dealt by the ultimate, with builds focused on attack speed, attack damage, the Zephyr, and ability power, it is clear that the Zephyr build will do the most overall damage, whilst applying black cleaver stacks in exactly 0.5s, providing you hit every shot. It is also a very good build in terms of utility, as it provides 40%cdr, meaning you can fire The Culling every 30seconds, and 40% movespeed which -without runes or masteries- will give you a very respectable 462 movespeed, for making sure you land every shot.