Time for Theorycrafting, Huzzah!
I'm going to assume that you want to maximize flat damage, before armour is taken into account, I'm also going to assume you're on Summoner's Rift, because most people are.
To achieve maximal damage, we'll need to consider the shots fired cap of 34. Given a base speed of .638, and a formula of 7.5+10.5*AS=shots, we'll need a 395% bonus to reach the cap. Lucian gains 3.3% AS a level, so after 17 levels, he's earned 56% AS. Using the Fury and Frenzy Masteries, he earns another 14%, so he's at 70% before we have to make any real choices, leaving 325% to find.
Now, each bullet Lucian fires in The Culling deals 25% bonus attack damage, 10% bonus ability power, and, at level 18, 60 flat damage. Also, he will get a bonus attack every ~16.5% Attack Speed.
Our ally choices are, for attack speed;
Nunu (45%), Ezreal (40%), Sivir (30%), Jarvan IV (22%)
for attack damage;
Janna (50), Taric (35), Sona (20)
This means that Nunu is a given, Hello Nunu! Would you mind carrying auras for me? Thanks! (280% AS remaining)
Nunu picks up Will of the Ancients, which gives us 30 Ability power, Zekes Herald, which gives us 20 damage, and, for good measure, Black Cleaver, which shreds enemy armour for 5% a hit, stacking up to 5 times. (I know I was ignoring armour, but this doesn't hurt anything.)
Now for masteries, we spec at least 26 in the offensive tree to pick up the following:
Summoner's Wrath: 5 AD, 5AP
Fury: 4% AS (mentioned above)
Frenzy: 10% AS on crit (mentioned above)
Deadliness: 12 AD
Blast: 18 AP
Havoc: 2% Damage
Brute Force: 3 AD
Mental Force: 6 AP
Archmage: 5% AP
Executioner 5% Damage
Our totals right now are:
115% Attack Speed (280% Remaining)
59+5% Ability Power
40 Bonus Attack Damage
7% Damage multiplier
Now, relevant damage items are, a stacked Sword of The Occult, and stacked Bloodthirsters. These give 110 and 100 attack damage respectively, and Bloodthirster can be purchased multiple times.
Relevant speed items are, Zephyr (50% AS, 25 AD), Runaan's Hurricane (70% AS), Fully activated/stacked Guinsoo's Rageblade (52% AS, 77 AP, 35 AD)
These items make Ezreal, Sivir, and Janna the most effective allies in terms of item replacement value, between them they give 70% Attack Speed (210% remaining) and 50 Attack Damage.
My interpretation is that this remaining 210% Attack Speed is most efficiently bridged with 2 Runaan's Hurricanes, a Guinsoo's Rageblade, and 18% Attack Speed from runes. This leaves 310 Attack Damage from a Sword of the Occult and two Bloodthirsters.
Our totals at the moment are:
377% Attack Speed (18% remaining)
132+5%=138.6 Ability Power
385 Bonus Attack Damage
7% Damage Multiplier
Now for Runes, we want 1 Glyph of Critical Strike Chance (for Frenzy), 8 Glyphs of Attack Speed (worth 5.2%) 9 Seals of Attack Speed (worth 6.8%) and 1 Quintessence of Attack Speed (worth 3.4%) This brings our Attack Speed to the cap, and we fill out with 2 Quintessences of Might (9 AD), and 9 Marks of Might (21 AD)
We also can't forget Elixer of Fortitude, for another 15 attack damage, and Exalted with Baron Nashor, for 40 attack damage and ap
Our final total stats are:
395% Attack Speed
445 Bonus Attack Damage
7% Damage Multiplier
Plugging this in to The Culling's formula, we get (2040 + 8.5*445 + 3.4*180.6)*1.07 = A whopping 6,887.9 Damage!
This is well under the 10000 you mentioned, unless you factor in the quadruple damage to minions, but it's a lot to dish out in 3 seconds while moving.