Attack Speed is by far Lucian's least favorite stat (despite it being used in The Culling). The reason for this is because Lucian's normal attack pattern is: ability>auto>>repeat. Because his passive is his main source of damage (combined with regular auto for two shot), and that does not scale off of AS. As such, I itemize Lucian in a way that does not involve AS. Just look at what I gave (and didn't give) him for his runes. There are no Greater Quintessence of Attack Speed in this build (despite them being pretty strong right now), and instead you see Greater Quintessence of Armor because of Lucian's lower attack range he can get poked a lot by autos during the early game (when your spells still aren't ranked up). Also note the way that I built him item-wise. The only zeal-based item I have for him is Trinity Force (the one with the lowest attack speed out of the three), to mostly synergize with his attack pattern (ability>auto>>repeat). While the other attack speed item being Youmuu's Ghostblade, which grants attack and movement speed upon activation. This can either be used for a trade, chasing/kiting, escaping, or during your The Culling. This gives Youmuu's Ghostblade lots of versatility through it's many uses. Then there is the occasional Blade of the Ruined King, which while having less AD and LS (and cost efficiency) than Bloodthirster as well as having attack speed (which I just explained that Lucian doesn't really need) still can have it's uses. For one Blade of the Ruined King's passive (8% current champion health damage) scales very well off of attack speed (again a stat that you should not get on Lucian), however it can also (not as much) scale off of the fact that you have a double shot from your Lightslinger (second shot only deals 50% AD so AD is only worth 75% of it's value between both shots, whereas the 8% current champion health remains 8% on both shots). But personally I think that more is lost than gained from choosing Blade of the Ruined King over Bloodthirster, so it's really up to you to decide

Your only two options are: Greater Seal of Health and Greater Seal of Scaling Armor. Simply put the Greater Seal of Health is great to be paired up with Greater Quintessence of Armor during the early game, while the Greater Seal of Scaling Armor goes well as of late game when you have health from Trinity Force (250 health) and effective health from Bloodthirster (shield passive and 20% life steal).

They are not serious builds, I just forget things so I put them on MobaFire. If you must know it spawned out of the idea that Lucian does not need AS, just CSC and AD (also ArPen) because he does auto>>ability>>auto>>ability (etc.) and his Lightslinger passive hit scales off of CSC/CSD.