Ok, so I'm going to take a constructive approach to your build, and other builds. And attempt to explain why some people won't prefer your build.
, in general, works like a caster adc. This is because his passive allows him to double strike. So each time you use an ability, you get two free auto's (your regular auto attack plus one at (30/40/50% AD) + it can crit). So this gives him the ability to fight within these mini power spike windows, giving him the ability to out trade his opponents by dash - double - q - double - w - double - dash - double (and you can throw in an ult if you want for another quick double).
ok, so the items you listed are : 
.
I assume you add a 6th defensive item since you don't list it and finish build something like this
( 
/ 
/ 
).
{quoted}
Im far from a great player, but I do main Lucian and I have been using Essence Reaver + Ionian Boots + Brutalizer, which if anyone can notice is 10% + 10% + 10% Cool Down Reduction. Plus a handsome 10% lifesteal and 10% armor pen !!!!!
- gives a flat 10 armor pen, not %. Which is actually better for the early game and for killing champs that don't build armor. = +20. Although a 
more than negates this penetration ( gives 40 armor!). Which is why you do, rightly, get a . I like this item decently, the active has synergy with your ult, allows you that extra attack speed, gives you cooldowns for your abilities, helps you stick to targets, and gives you some crit for your auto's (and passive). It may fall off late late game, but gives a really good mid game power spike that can hold you until you are ready to swap items out. (note that 
is probably the better dueling item with 20% more crit chance and 10% more AS than the ghostblade active. However, you are not taking your lane bully with CDR and Flat Pen. It's really a style choice that early. How do you want to play.)
- I like these boots on Lucian. This and ghostblade bring you up to a good amount of CDR without really overdoing it. If you pick up a blue buff while killing people you will be set on cdr without toppling the scale for no reason. 
are also fine if you are more focused on your auto attacks, however since you generally throttle your damage using your passive and Ghostblade gives you 6 seconds of +40% AS, i just think the Ionian boots do a better job of letting me maximize my damage.
- this is a standard adc item. If the enemy team has armor then you need this to do damage. Even 
uses this so that all 3 of her attacks can be useful instead of just her silver bolts proc.
- again pretty standard for a late game pick up. Does good damage, gives 20% lifesteal, and provides a shield to help negate random harass if your team sieges.
- this would be the main item people would have issues with, me being one of those people. So let me break down why. Choosing to Rush this item means, obviously, you are not rushing other big starting items. The big starting items like this all have +80 AD so that is even among all of them. So you are basically rushing the passives. 10% cdr, 10% lifesteal, get mana back on hit 2% - 8%.
You can get 8% lifesteal and 10 damage on 
for 800 gold, you can easily get the lifesteal if you are behind and need it and still build towards other items.
10% cdr I do not think is better than either a 
active or 
giving you a 20% chance to deal 250% damage.
Mana back- I don't find mana to be a huge issue, especially late game, as long as you know how to watch your mana pool. If you are spamming your abilities all day long then yeah, you will run out if you don't have blue buff. Mana is also only a problem if you are doing an incredibly long duel. You should not have a problem cycling through your abilities a few times in a teamfight. The reason I don't like this passive is because it makes up for not being able to manage your mana, something that you can learn to do therefore you don't really need to spend gold on it. This is an exception on some champions. The biggest example I have seen is 
, who can justify spamming his gate + orb. So in a long siege sequence he may need this.
I think that the lifesteal is negate-able with and blue buff can make up for the other passives mid - late game when you may possibly be spamming that much without going home. Generally you take this blue off somebody you killed, or you steal their blue.
Why isn't this build used more if Lucian gets ahead a little ?
I would say this is because you can rush a 
item better suited to gaining early dominance with your passive. Such as (those crits).
So we have a Lucian with TONS of armor pen, TONS of Life Steal and virtually zero cool down compared to enemy champs, and with essence reaver constantly supplying mana, I spam abilities all day
Your armor pen is about the same as most late game builds as does not do a % as you thought. It is actually better that it does flat as that is more effective against the non armor champs (mentioned earlier).
The difference between having 20% lifesteal and 30% lifesteal really isn't that big if you don't have the damage to back it up. Remember, you are building to spam abilities which will not proc lifesteal. You need better auto's to make the lifesteal pay off.
The last part about spamming, again, is just learning to manage your mana / abilities, and is negated by having a blue buff. Which means any blue buffs you pick up with your current build are actually pretty useless.
What is wrong with this build ?
There is nothing really wrong with the build. You are building to spam abilities and you can do that. However, you are susceptible to burst damage and you don't have that burst healing from crit strikes (not consistent) and you don't do burst damage (low crit), you do chunks with your abilities. This is fine, it can work especially if it fits your play style. However, I think this style can be maintained while covering some of the weaknesses if you just get a blue buff (which you will by playing teamfights well).
Ok, so if I'm so smart how do I build?
.
This gives me 20% cdr, 35% crit chance, 20 armor pen (plus runes/masteries), and 6 seconds of AS/MS with active.
/
Order depending on enemy armor and focus / kill potential. The extra 50% AS, 35% crit, and minion ignore passive helps dueling a lot. 70% crit strike with a 6 second window of 90% AS. This combined with my abilities giving me extra chances for Crit Strikes generally means that the fight is over by the time one rotation is over. That is e - 2 (autos) - q - 2- w - 2- e - 2. Then 90% AS, Ulting them if they run. 8 auto's there, at 70%, good chance i'm critting them 4-5 times real fast.
The % armor pen is there for the same reason it is on every adc. It is great against people who have bought at least 1 .
Last item can def go depending on the game. Defense options as listed above :
- if you are being focused / bursted and can't stop it.
- to shrug off that 1 form of CC that can get you.
- Actually a good MR and dueling item. 55 MR. 450 health. 100% base regen. Gives you more of a life bar to fill back up with lifesteal if you swap out for / / even if you want.
You can also get items like 
if you aren't afraid of being killed and want the extra burst + 90% Crit Strike. ( can give you the 100% or 
can give you the sheen proc.) You can also sell boots for these extra damage spikes if you need them, as they all give MS (though not as much as 
which also gives AD and preserves your cooldowns).
also gives damage and champion only lifesteal (10%) for those short duels. Doing crit bursts should give you enough healing with this.
One of the glaring weaknesses in this build is the lack of sustain / lifesteal. But I supplement that early game with potions. This is also deliberate as the playstyle I am choosing is that of a burst / nuker. If the game looks like one where I will need the sustain, I can always supplement with a instead of the first or .
What about the ol' / ?
This build usually finishes out like the other builds (
, , / , extra slot) but is focused on having a really rapid fire ult and kiting potential with the two actives.
You can also make fun on hit builds with , 
, 
, 
, that type of stuff. I haven't tried it, and i'm not saying it's the strongest build. It could be fun on aram/bots though!
Ok, so that was long. I hope it was helpful! If you have any questions or if I need to clarify something please let me know and good luck out on that Rift!
