Ive tried like basically every Item in the game for APC Lux with a playstyle that expects you to only hit e and r (as if you dont have a q, since i play in master - grandmaster range). (we ignore Support and hate Midlane Lux because its flawed)

I Noticed for practical usage (no mana problems) this deals the most damage since like 3 months now:

Damage Rune

with: Stormsurge, Mejais, Actualizer, Rabadons, Malignance, (void would deal more raw damage, but practical:) Cryptbloom

now the Haste versions are: (yes aery, because comet on your ult alone is not consistent)

Haste runes

Haste Build: literally the same except instead of Stormsurge i go Seraphs because we dont have any mana runes here.

Now i do happen to have cooldown problems later in the game sometimes when my team really like REALLY doesnt want to win, so i need to kill the enemy and then def them alone in the next 20 seconds after that, into them ending, which wihtout r bc i already killed someone with it is obviously impossible. Haste would help here and in similar situations (meaning maximizing the potential of lux, which is what we want to do here.)

now after trying every combination of both builds we get the following numbers:
cooldown is that of lux r and damage calculations based on using e and r as lvl 18 Lux on 70mr target dummy for realistic average value.)

DMG Build + haste runes: 2700 cd: 18,69
Haste build + runes: 2344 cd: 16,74
ALL DMG build: 3066 cd: 24
Haste build + DMG runes: 2674 cd: 21

1. DMG Build + Haste Runes (The Winner)

• Total Damage: 2700
• Expected Damage (70% hit rate): 1890
• Cooldown: 18.69 seconds
• Effective DPS: 1890 ÷ 18.69 = 101.12 Damage per second

2. Haste Build + Runes

• Total Damage: 2344
• Expected Damage (70% hit rate): 1640.8
• Cooldown: 16.74 seconds
• Effective DPS: 1640.8 ÷ 16.74 = 98.02 Damage per second

3. ALL DMG Build

• Total Damage: 3066
• Expected Damage (70% hit rate): 2146.2
• Cooldown: 24 seconds
• Effective DPS: 2146.2 ÷ 24 = 89.43 Damage per second

4. Haste Build + DMG Runes

• Total Damage: 2674
• Expected Damage (70% hit rate): 1871.8
• Cooldown: 21 seconds
• Effective DPS: 1871.8 ÷ 21 = 89.13 Damage per second

Based on these i asked in this case gemini 3.1 Pro to take into account (the kinda complicated) matter of that i cant actually hit the enemy on cooldown with my spells and it came up with this intresting theory/rule of thumb:

The "Fixed Opportunity" Rule

Imagine you only get a good opportunity to combo an enemy every 25 seconds (e.g., waiting for waves, sweeping vision, or dancing around objectives).

• DMG + Haste Runes: Ready in 18.69s. (Sits unused for ~6 seconds). Expected Damage: 1890
• ALL DMG Build: Ready in 24s. (Sits unused for ~1 second). Expected Damage: 2146

Result: If your chances to hit someone happen 24 seconds or more apart, the ALL DMG Build dominates everything else. The cooldowns don't matter because both builds will be ready in time for the fight, but the ALL DMG build hits significantly harder when that rare opportunity arrives.

The "Hold Time" Break-Even Point

What if you are constantly looking to fight, but it just takes a few seconds to line up a shot after your spell comes off cooldown?

Mathematically, the ALL DMG Build overtakes the DMG + Haste Runes build if you hold onto your spells for an average of 20.5 seconds after they come off cooldown.

• If you wait less than 20 seconds to fire after your R lights up -> DMG + Haste is better.
• If you wait more than 20 seconds to fire after your R lights up -> ALL DMG is better.

(Note: The full Haste builds fall completely out of the race here. Since you are holding spells anyway, their only advantage—extreme spamming—is entirely wasted).

TLDR: This means basically since while you fight chances are likely that you will hit a spell in 15 seconds after your ult came back up and therefor it is actually best to take haste in runes and damage in items,

even on a champion like lux, that has very rare opportunities to garantee a spell hit.

(btw you can find my Accounts if you search this Accounts Name)

EDIT: As a result the mathematically correct build for lux is currently:

https://preview.redd.it/7mau1kba4yhh1.png?width=799&format=png&auto=webp&s=3c887d9f1bb30fedb96603336c4f5b3a92f6bdee

with the following build (copy this text and paste it into the field from the items menu "Paste copied set"):

{"title":"WeaksideParadises Lux Build","associatedMaps":[11],"associatedChampions":[99],"blocks":[{"items":[{"id":"1056","count":1}],"type":"Start"},{"items":[{"id":"1082","count":1},{"id":"1052","count":1}],"type":"First Base"},{"items":[{"id":"3145","count":1},{"id":"1001","count":1},{"id":"1052","count":1}],"type":"Second Base"},{"items":[{"id":"3113","count":1},{"id":"1027","count":1},{"id":"3041","count":1}],"type":"3rd Base"},{"items":[{"id":"3020","count":1}],"type":"Boots"},{"items":[{"id":"4646","count":1},{"id":"3802","count":1}],"type":"1. Item"},{"items":[{"id":"3041","count":1}],"type":"2. Item"},{"items":[{"id":"2522","count":1},{"id":"1027","count":1}],"type":"3. Item"},{"items":[{"id":"3089","count":1}],"type":"4. Item"},{"items":[{"id":"3118","count":1}],"type":"5. Item"},{"items":[{"id":"3137","count":1},{"id":"3157","count":1}],"type":"6. Item"}]}

Funny Streamer Reaction for the memes:

Thats some nice damage

https://www.twitch.tv/jankos/clip/FamousQuaintEmuRlyTho-XJutz4wz4YvlUhma

What even killed me, this lux is a big problem

https://www.twitch.tv/jankos/clip/CrepuscularVibrantOysterFunRun-Tt858XuSDARmqc7N