Welcome to my first guide, this one is about how to play Lucian as a top-laner with all-blue items.
Note that this is my way and my friends way on how to play him as top, you can try other things yourself, and change the build up a bit or anything, but this is a guide on how to play with my experience with him. I have yet to play him more often, but this is information that I have gotten so far by playing him with this specific build.

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Lore

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Lucian wields relic weapons imbued with ancient power and stands a stalwart guardian against the undead. His cold conviction never wavers, even in the face of the maddening horrors he destroys beneath his hail of purifying fire. Lucian walks alone on a grim mission: to purge the spirits of those ensnared in undeath, his eternal beloved among them.

Like the twin relic weapons they wielded, Lucian and his wife Senna were carved from the same stone. Together they battled evil in Runeterra for years, bringing light to darkness and purging those taken by corruption. They were beacons of righteousness: Senna's dedication to their cause never faltered, while Lucian's kindness and warmth touched the hearts of the many lives they saved. Two parts of one whole, they were devoted and inseparable.

Though Lucian and Senna witnessed terror that would break most warriors, nothing they had seen compared to the horrors wrought by the Shadow Isles. When the spectral denizens of that accursed place began to manifest across Runeterra, Lucian and Senna hunted them down wherever they appeared. It was grim work, but the fearless pair prevailed until one tragic encounter with the soul-collector Thresh. Lucian and Senna had faced such nightmarish undead before, but never one so deviously clever and cruel. As the terrible battle unfolded, Thresh sprung an unexpected ploy. To Lucian's horror, the creature tricked Senna and ensnared her soul, trapping her in a spectral prison.

Nothing could bring her back. Senna was lost, and for the first time, Lucian faced his mission alone.

Though the Warden had taken half of Lucian's heart, he had also created the Shadow Isles' most dangerous foe. Lucian became a man of dark determination, one who would stop at nothing to purge the undead from the face of Runeterra. In honor of Senna's memory, he took up her fallen weapon and vowed to see their mission through to the end. Now wielding both relic weapons, Lucian fights to slay the undead and cleanse the souls of the Shadow Isles. He knows that Senna's soul is lost, but never loses hope that one day he will bring her peace.

"Be grateful. By slaying you now, I spare you an eternity of torment"

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Pros

Great kiting potential with the new low CD on his E with the CDR items while also removing slows.

The enemy might think that Lucian is going full AD, therefor building lots of armor, but has hybrid damage thanks to Iceborn Gauntlet, making his W very useful.

Keeps alot of his Attack Speed with BotRK and Youmuu's Ghostblade which makes his ult still very effective.

Great at split pushing thanks to his low CD's meaning he can use The Culling every 30 seconds with 40% CD reduction.

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Cons

Blucian lacks high burst damage.

Champions with On-target CC such as Taric's stun, Vi's Ultimate etc, can shut him down pretty well.

Is very vulnerable to AP burst champs (like every Adc) such as Fizz, Leblanc etc, but can still outplay them if you know how to dodge ;P.

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Masteries
Everything is pretty clear, you do the same in Offensive like every other Adc mastery page, but instead of going full defensive, you get the extra movement speed in Utility for even more potential in kiting, while losing a fraction of health instead.

9x Marks of Attack Damage
9x Glyph of Magic Resist
9x Seals of Armor
3x Greater Quintessence of Attack Damage

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(Pretty standard Rune Page, feel free to change it up a bit... or alot.)
The Attack Damage on the Marks and Quintessence's is pretty obvious, helps alot with last hitting and of course, dealing more damage with spells and whatnot.

Magic Resist Glyph's to help against the high AP burst champions that every ADC fears.

Armor is for... yup, you guest it.

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Maxing Q immediately is pretty crucial when playing Lucian cause of the high poking ability that he has throughout the game (and pushing power). I have not tried to max W first, and it could work when going up against a full armored target, I'm not sure yet but later on I will try it.
If you are dealing with a lot of slows in the enemy team, think about maxing E first so you can take advantage of the low CD and remove them.

If you are not split pushing, then you should be helping your team instead.
Like explained earlier, Lucian is pretty good when it comes to poking, and especially with the low CD on The Culling, you can use that to bring the enemy team low without the fight even starting yet, and have it back up when someone decides to engage.

Keep yourself out of the enemies reach, stay behind your team and use your range to kill them. If someone manages to come close to you, Use your E to dash away or dodge the enemy which should give your team enough time to do what must be done while you are kiting the one chasing you, or even kill the one chasing you.