As we know that Lucian is not out yet, this guide is based on my personal experience on general adc builds. So far, what we know about Lucian is quite limited and the information below may not be 100% correct. Please point me out if you find any mistakes. I will update this article when Lucian is released officially.
Lucian Guide (Work in Progress)
Flash and Barrier are two standard summoner spells for adc. Ofc you can also pick Flash + Cleanse if you are scared of the other team's CC.
PS: The images below are clickable for original size.
Standard AD Carry rune setup. Life-steal quints are good with a Doran's start. You generally won't be needing MR early game, so that's why you should get MR/Level instead of Flat MR.
Standard masteries for an ADC when using Barrier/Cleanse.
What this does is make you auto-attack twice (in the time it usually takes to hit once) after you use a spell. Lucian's passive is great for trading in lane. When fighting, try to make use of it after every spell cast, like you would with somebody like Lux(if you play her). This also does full damage to minions and monsters.
Q: Targetted line nuke that does less damage to minions. Will shoot as a straight line beween Lucian and his target. This will hit all enemies in a straight line(between Lucian and his target). Level this first(except for his ult!), because not only is this his hardest hitting spell, its AD ratio scaling also increases as you max the spell. At level 3, this spell's scaling is better than Lucian's W. Use this skill when the minions are running a straight line to hit 4 ~ 5 minions.
This shows the width of Lucian's Q:
W: Projectile skill-shot, similar to khazix's W. It goes in a straight line, colliding with the first target it hits, then exploding, doing damage to nearby enemies, also marking any enemies that it hits. Attacking marked enemies will grant you a flat movement speed bonus. This increases as you level it, so max it after Q. This spell gives Lucian some good kiting power, together with his E. You can proc this multiple times. However, the spell has a pretty long cooldown, so you might want to save it for a sticky situation.
This shows the approximate range of his AoE on his W (the visual effect grows bigger than the actual splash damage radius):
E: A short dash, similar in range to Vayne's Tumble. However, this can go through walls and removes all slows, which is good for escaping ganks when the jungler has slows like red buff. This has a very long cooldown at rank one, but maxing it earlier doesn't help as much as maxing the other skills. Use this sparingly, unless you're confident and want to use this to activate your passive. While you're ulting, and if you get a kill/assist, your E resets, so don't be too skimpy if you think you'll get a kill/assist while you're ulting.
R: Lucian's ultimate, a barrage of bullets that damages the first enemy it hits. Hard to use in the beginning, but if used properly, it can do a lot of dmg. With a full build, it does around 3,000+ damage if all the shots hit(probably won't happen). Activating it will make Lucian shoot in a direction(not at a specific point). It's hard to explain, but the direction you point it at, relative to Lucian is the direction Lucian will always shoot at(relative to Lucian). The catch here is that you won't be able to change where it's shooting at, so you have to be careful about where you aim it. This is a channeled ability, but you can still move and use your dash to adjust your position. This also does 3X the damage to minions, so you CAN clear waves very fast(imo it's a waste, though). You can also burn this skill to finish off red or blue, VERY quickly, almost with one ult later on.
When chasing, use your W and attack someone to get the movement speed bonus and activate your ult to help stay in range, and use E if needed/if you know you'll get a kill or assist, since it resets. You can also surprise someone while you're running away and do massive damage by ulting towards them while running back. This will scare them or force them to side-step.
NOTE: This skill scales off Attack Damage AND Attack Speed. It's better to build a mixture of both if you want to play Lucian like a one-trick pony.
A good skirmishing combo without using ult would be E > Auto > W > Auto > Q > Auto, or Q > Auto > W > Auto > E > Auto. This is hard to pull off early, because your attack speed is so low, but if you pull this off, it can do a lot of damage, making use of your passive.
To be updated...