How to Doom?

Doom is one of the best positions 3 in the game. Even if Doom starts with 0 armor, his standard build should be utility/tank. Scorched Earth helps a lot in this way, and by building a Mekansm and then a Shiva's Guard it turns Lucifer into a great utility who can outrun most of enemy heroes thanks to Scorched Earth and Shiva's Guard. Assault Cuirass is usually the next step into the collection of Auras. His ultimate Doom has very few to be explained, since it's the most famous hard disable of the game. Use it on the hard carry or a key teamfight hero (Enigma, Tidehunter, Magnus, Faceless Void, etc). Eat the big jungle wolf to gain a +30% atk Aura and a passive crit for yourself, then remeber to eat only creeps with no skills to avoid an override.

Doom is anything but a rightclick carry. He is a tanky initiator hero with very good farm speed.

Strengths

Incredible farming speed thanks to Devour. With a Hand of Midas he is one of the best farmers in the entire game, but even without a Hand of Midas, he is capable of keeping up his farm really well.
He beats any hero in a 1v1 manfight. Doesn't matter what the enemy has, Doom can negate most of that with his ultimate.
Good starting stats, decent stat gains.

Weaknesses

Paper armor. His good starting strength makes him capable in the early game, but as the game progresses he needs to get either an Assault Cuirass or a Shiva's Guard to boost your EHP.
Awful mana pool. This is one of the biggest issues of Doom. He simply needs something to boost his complete mana pool.

Where do you lane him?

Doom can be played anywhere between position 1-4. He can safelane farm, mid, offlane or even jungle as a position 4. You will have to of course choose the best creeps for the job. I am no Doom expert tho, so I really don't want to talk about this too.

What do I build as Doom?

Well that all depends on the situation. I will just note a few items that generally work on Doom.

Blink Dagger: Blink ensures you great initiation power. Nothing better than starting the fight by taking the enemy's initiator completely out of it.
Shadow Blade: Same thing as Blink, probably a bit inferior to that. The Blink mana cost removal buff really made this item a weaker choice on Doom.
Shiva's Guard: Solves mana and armor problems at once. Also great in combination with Blink . Makes you a great initiator.
Black King Bar: I have to say this is a complete necessarity on Doom. You have to be in the middle of the fight and get all your spells and items off. You can't afford being disabled by some stupid spell like a 4 second chaos bolt or a long ass Frostbite. Doom needs to run at people and he can only do that while being golden and shiny.
Refresher Orb: Are there two heroes that cause problems in a fight? Get this item then. You will need a way to increase your mana pool or else you wont be able to make enough out of the item.
Scythe of Vyse: Always an awesome item, just really hard to farm up. Doom can most certainly afford it so why not build one?
Aghanim's Scepter: I would only get this if there is a hero that just does not care about being doomed. Like a really farmed Wraith King. He will just tank the doom and keep on right clicking people. I still can't really imagine it being picked up in most cases.
Mekansm: It's just like Scythe of Vyse. Really good item, but there is usually not many heroes to farm it up early enough for the team. Doom can do just that and lead the team into an early 5 man push with a Mekansm and some Arcane Boots.
Hand of Midas: More money.