This guide does not focus on Lucian in general and does not cover his mechanics/playstyle. Its focused on showing the new emerging build for Lucian and how its different from the old one. I dont take credit for coming up with this.
This vid sums the build up, probably better then the guide:
https://youtu.be/mJ2E9Io8gEs
Gosu playing with it:
https://youtu.be/urHKT-q2iuE

Build Pros:
+ Amazing armor pen, killing tanks is ez
+ Lucian ult deals damage
+ Can be more tanky then on average
+ High q damage, very good poke early
+ Ghostblade active
Cons:
- May run into mana issues early and when spaming abilities
- Not many crits, autos may hurt less

This item build will make you more pure AD focused compared to AS or crits. Since lucians kit allows him to naturally output a lot of attacks (passive autos and ulti) it synergises with Black Cleaver really well making getting the 30% armor reduction on enemies very easy to achieve. Add in some flat armor pen from Ghostblade and you can almost feel like Vayne. BC and Ghostblade also both give you move speed (Ghostblade active + BC passive ) Add in swifty boots and you can almost feel like a Master Yi
This build path is also very stat efficient:

Credit goes to Phylol for the stats below

Ghostblade +BC:
115 AD
30% CDR
45% AS (Ghostblade active)
300 HP
20 flat A pen
30% A pen
20% MS
Overall core cost= 6300

Compared to the standard Essence Reaver + RFC core

65 AD
30% CDR
30% AS
50% crit
Long range auto
5% MS
Overall cost= 6200

For 100 more gold you get a lot more raw stats that help you to win lane and also work well in the late game.

Not many things are different with this build. In lane you should focus more on your q poke (as you do with Lucian anyways) as with the armor pen and AD it will hurt a lot. You must watch out not to run out of mana without ER . Your q will do more damage then normally with this build so landing it becomes impoetant throughout the game in general as your autos will not crit as much so make the q shots count.

With the BC,Ghostbalde core your ulti will start to deal good damage. It can be used in mid/late game to shred tank armor and its large range makes it a good opening tool. It will also speed you up with the BC passive so it can be used as an escape tool.

Apart fron that your playstyle remains the same, try to not get killed by all the assasins and combo passive with abilities to deal damage and recharge your dash.