AP ratio matters mostly when you, you know, have AP, so during the lane, Lux's ult deals way more damage than Neeko, and her whole combo deals way more damage.
Also, Lux's Q is only partially blocked by minions, as it roots 2 people, not just 1, so unless you have 2 or more minions between you two, she won't root, but that also points that no Lux will throw Q when there are so many minions, increasing the chances that she will hit.
Lux's combo at level 6 deals with just a Lost Chapter and Doran's Ring, aka 55 AP, and the 20 from stats equaling 75:
Q: 70 + 0.7 AP = 70 + 53.5 = 123.5
E: 150 + 0.6 AP = 150 + 45 = 195
P: 70 + 0.2 AP = 70 + 15 = 85
R: 300 + 0.75 = 300 + 56.25 = 356.25
P: 70 + 0.2 AP = 85
Total - 844.75
That's a "standard combo" without microing her passive, if she does, it's:
Q: 70 + 0.7 AP
P: 70 + 0.2 AP
E: 150 + 0.6 AP
P: 70 + 0.2 AP
R: 300 + 0.75
P: 70 + 02 AP
Total - 844.75 + 85 (just add another passive proc) = 929.75
Now Neeko's level 6 combo, same items and runes:
(will go with total damage for Q, since it's assuming all 3 pops hit)
Q: 310 + 0.9 AP = 310 + 67.5 = 377.5
E: 80 + 0.4 AP = 80 + 30 = 110
R: 200 + 1.3 AP = 200 + 97.5 = 297.5
Total - 785. 59.75 lower than Lux's basic combo
And if Neeko also hits her W passive 3rd hit, we add:
W (P): 50 + 0.6 AP = 50 + 45 = 95
Total - 880 - 49.75 lower than Lux's combo when microing her passive, but 35.25 higher than Lux's basic combo
So yea, Lux totally outdamages Neeko in a combo as that 50/60 damage is more than enough to get kills Neeko would not get, and has better harass range. And since Lux's Q passes through 1 minion, if a Lux is good, she can aim in well enough for you to think you're safe and get him still.
Your argument was that "Neeko will hit her E eventually and you will die", mine was that "Well, so can Lux, and you're more dead to her than to Neeko" in the early game. Also, not to mention that even if Neeko hits her E, she still has to come close to use R, Lux doesn't really. Assuming Lux decides to say "screw it" to her 2nd P proc after R, she will deal almost 25 less damage than a Neeko combo without her W (P) and being very safe, while Neeko has to actually go and be in danger.
"But late-game her ult deals more damage"
So what? To get to a 6 item power spike, she needs farm and kills, but it's much harder for her than for Lux, so most of the time, a Neeko vs Lux will have the Lux be ahead of Neeko until that 6 item power spike because she can get more kill early on the enemy laner, their ganks are equally good, even tho Neeko can change the way she looks, a smart enemy should not let her get close regardless, so she still has to use her E from a longer range, but then, there's nothing different about it compared to Lux, who, can also use her Q to make her E an easier hit.
So yea, even tho Neeko has a better ratio on her R, her combo deals less than Lux until late in the game.
. None of these mages will cancel their ults on any condition but their own death, sometimes not even then.
's ult has an identity of always finishing unless she dies mid cast. That's the same exact rules as Neeko's ult.
lvl 1 Q is 210 +135%ap
lvl 1 R is 180 +105%ap if 3 people all get hit its 540 +315%ap
lvl 1 R is 150 +150%ap
lvl 1 R is 125 +75%ap but if a target is below 30% it becomes 250 +150%
lvl 1 R is 625 +225%ap
lvl 1 R is weird due to the range thing 150 to 300 and 80%ap to 120%ap
lvl 1 R 420 +120%ap without any upgrades
lvl 1 R 503 +183%ap rocket ult
lvl 1 R 250 +75%ap a bit low for this but adding it because it will always hit 5 people
lvl 1 R 200 +100%ap
lvl 1 R 200 +130%ap
lvl 1 R 625 +250%ap
lvl 1 R 450 +125%ap
lvl 1 R 490 +305%ap
lvl 1 R 200 +73%ap middle is 300+ 110%ap
lvl 1 Q 125 +150%ap
and 
