Manamune is actually good on him for a variety of reasons.
Lucians main weakness in early lane is limited trade due to mana, in combination with wave control related to that— and of course short range.
Lucian also scales heavily off of ad. Which manamune offers more early, and scales.
Lucian also likes to build cleaver. Lucian also likes to build bork.
Bork makes sense to build later, when the enemy has more health. Also remember that bork is 8% CURRENT hp. So it actually becomes far worse as the enemy has less health. Making it also far more valuable when the enemy has far more health. Thats when it shines.
Bork and manamune do additional ad dmg on hit.
Meaning:
Build manamune, cleaver, bork, doms/mortal.
They all synergize. Lucian stacks manamune between 20-25, it has more ad than bork and nearly infinite mana for spamming trades and lane control.
Manaumune will have around 80 ad when stacked, then about 160 on hit. Bork is better over 1600ish health, manamune is better below that, we're covering all the bases. Pen just increases all the on hit effects, lucian hits about 9 a rotation. It hits hard enough that you don't need crit and it doesn't fall off. You can kill any tank, sej, mundo, amumu, it shreds everything and its really cheap.
I like to run pta and futures market, free boots.
Even behind you're ahead on items, you are consistently strong throughout the game. Hard spike around 25 minutes, lucian is designed for crazy on hit builds. Even if you get hit by anti attack speed items, nasus, it doesn't matter.
It does kinda fall off if you get into like 50+ minute games. In those cases you just go gathering storm and build the same.
You ult SHREDS anything.