Well, with Lucian you have several options. I'll go through them and why I think Manamune is a superior options.

1. Bloodthirster. This is one conventional start. Basically you go for maxing his burst damage with his autoattack combos. This is great for a bursty kill lane, but if your lane gets pushed you will probably get screwed. Because of Lucian's shorter range he cannot farm effectively with auto attacks when being aggressively pushed - and you will quickly run out of mana trying to clear with your abilities. If that isn't a problem, then this is an excellent start.
2. Trinity Force. Classic Lucian start. The only beef I have here is that Sheen or Phage is not going to give anymore sustain, and the added damage for your burst from Sheen is hardly worth the loss of extra attack power early on. Ultimately if you get fed in the first 5 minutes or so, you want to use that money for something that gives you more of an upper hand.
3. Blade of the Ruined King. This is a great item for Lucian, but a weird item to start with. The sustain is excellent, and you will certainly have a lot of solo potential, for what it's worth. The only time I'd ever go for something like this is if I was dealing with a double bruiser lane bot or something.

So what about Manamune?

- Tear of the Goddess is easy to pick up early at 700g, even if you get pushed out of lane.
- With Tear of the Goddess you can manage being pushed a lot better because you Q minion waves regularly and not worry about running out of mana.
- With Tear of the Goddess you can continually harass your enemy laners and you *will* out sustain their pots.
- With Tear of the Goddess you can still afford to pick up that Long Sword for a little extra early damage - about as good as getting Phage, minus the HP - which really doesn't help you early anyway. You don't need HP, as unless you manage to finish the enemy laners with your combos you're going to die anyway.
- When you start building Trinity Force you can pick up the Sapphire Crystal first, which gives you a healthy +4 attack power.
- Manamune scales with your levels in lane. This means that you are no longer bound by the power spikes that occur when you are able to go back. You will start to out scale the enemy simply by being there in lane. That gives you the power to push harder, and puts pressure on the enemy laners to have to back, which is not possible for them easily when their lane is pushed.
- Manamune continues to scale into the later game, which means once you have Trinity Force you won't suffer from the usual stutter in your damage between building Trinity Force and the next item.
- Your next item after Trinity Force can be Last Whisper or Blade of the Ruined King, increasing your potential targets to include tanky builds, and you should still deal good enough damage without having to build an attack item like Bloodthirster.
- In the late game, activating Muramana gives you a huge damage boost that will put you head and shoulder above your enemy carry. Sure, it costs you a lot of mana, but by this point with Trinity Force your mana pool should be so large that you can last through an entire team fight with this item active.

The one disadvantage Manamune has is that you are building it instead of Vampiric Scepter for the sustain, or instead of taking lifesteal runes and building B. F. Sword first. It's true that it will reduce your lane kill potential early on when you build Tear of the Goddess, but the flexibility it gives you in being able to farm your lane and negate pressure from enemy laners makes it worth sitting through 5 minutes or so of farm lane until you can pick up Manamune.