Why doesn't Vladimir use Life Steal items?

You mustn't mix up life steal and spell vamp.

Life steal steals on physical damage (meaning auto-attack for vlad). In fights, you very rarely use your auto-attacks to deal big damage because you're a caster.

Spell vamp steals on magical damage (meaning all of his spells), this is want you want if your plan is to steal more life.

• Zhonya's Hourglass is great because vlad's ult has low range but must be cast in battle engage to hit the most enemies and for the 15% extra magical damage. The two second invulnerability will allow you to stay alive in the heart of the battle if you get targeted.
• I also very often use Hextech Revolver with Vlad, but you need some AP. It's no use having 50% Spell vamp if you don't deal any damage.

Vlad spells cost life, the good thing about more spell vamp is you can get your life back faster with transfusions minion lines and you can cast life costing spells (specially Tides of Blood that stacks) with less impact on your life.

EDIT : I went to have a quick look at all the different Vlad builds. All (or nearly all) of the descent builds have hextech revolver in them with its evolution to will of the ancients - give more AP, more spell vamp and an aura :-)

• Rylai's enable you to slow enemies and get the kills you deserve. Vlad is really a slow guy and once the enemy runs, fight is done.
• Rabadon's better cause Vlad's damage are magical, mostly. Plus the passive is more rewarding for little AP increase than AD.
• Zhonya's Hourglass is a real asset in battle. Usually, Vlad's the first target, the hourglass can give you the seconds you need to cast your ultimate and provide your team a huge chance to win.

I usually don't take life steal items because Vlad's main attacks are not physical damage, but spells. You would better profit a spell vamp item like the revolver or the will of the ancient.

It's not that the passive is better than spell-vamp. It's that he has some nice drain on his Q already to survive. Getting items with both Health & AP makes the most out of his passive, which is the reason they're recommended.

Season 4 Vladimir:

• Will of The Ancients (WoTA) - Great item. Gives +80 AP +10% Cooldown +20% Spell-vamp making it a great aggressive item. It's relatively cheap and it adds amazing lane-sustain to Vlad even before completing (i.e. Revolver) allowing him to stay in lane and farm for as long as he needs.
• Zhonya's Hourglass - Great Defensive Item. Gives +50 Armor +120 AP. Gives nice amount of armor considering top-lane is commonly an AD champion. The best part is the 2.5s of invulnerability. On top of Vlad's great sustain, his built in invulnerability (W - Sanguine Pool), and this. You'll be pretty hard (and annoying) to kill.
• Rabadon's Deathcap - Great Offensive Item. +120 AP and a passive that boosts your AP by 30% meaning you receive +36 additional AP immediately. Gives significant pain to all of your skills.
• Rylai's Crystal Scepter - Nice Round Item. Gives +100 AP +400 HP and a Slow to all of your spells. Not only does this work well with Vlad's passive giving him an extra +10 AP and + 140 HP it adds 20.25 damage per half-second to his W - Sanguine Pool (This includes the Stats from the scepter and his passive due directly to the scepter). So this is a nice boost to his Sanguine Pool.
• Liandry's Torment - Nice offensive item for securing kills. +50 AP +300 HP +15 Magic Pen and a passive that does 2% of the targets current health over 3 seconds. In addition to +7.5 AP +70 HP from his Passive due to this item. It is nice for letting Vlad deal with those high health targets like Mundo or another Vladimir.
• Spirit Visage - Acceptable Defensive Item. +400 HP +55 Magic Resist +10% Cooldown Reduction +20 HP/5 Regen and a passive that increases Healing and Regen by 20%. Additionally + 10 AP from Vlad's passive. This is the go-to magic resist item for Vlad as increases Healing, reduces cooldowns, and increases HP. The healing passive stacks with Tides of Blood (E) and with applicable masteries.

Other things to keep in mind:

• Cooldown reduction - Allows Vlad to spam his skills more often. Additionally adds a lot more survival to Vlad as he is able to use his Sanguine Pool (W) and his Transfusion (Q) more often. Max CDR in combination with an hourglass can make Vladimir one unkillable champion.
• Ghost - Many people take Flash instead; however, I personally feel Ghost on Vladimir is a must. To be able to just Run in very fast, R->E->W->Q->E->Hourglass->Q->E->W->Q->etc->etc. is devastating. I've taken entire teams to their knees solo as Vladimir before.
• Farm - All of these items. They are expensive. Master farming as Vladimir and staying in lane. Farm, Farm, Farm, and Farm some more. Get those kills if you can all the gold helps you get there faster.
• Tranfusion (Q) - Minor note here. The healing from Tranfusion is a projectile and can be blocked by a projectile blocking wall such as Braum's Unbreakable or Yasuo's Wind Wall, he will deal damage but not be healed! Additionally, spell shields will block Tranfusion's damage but not the healing.
• Sanguine Pool (W) - It costs 20% of your current health. So if you're full health do not use pool to dodge a skill-shot or stun that won't result in you losing 20% or more of your health, you're basically harassing yourself. Don't use your W to farm either, it's just not worth it. Auto-attack appropriately until your E and Q are off cooldown. Notes: While Sanguine Pool (W) is active Vlad is: not affected by Auras (positive or negative), still going to take damage from Damage-over-Time (DoT) effects such as poison, ignite, Swain's Torment (E), etc., still blocked by temporary terrain (Anivia wall, Trundle Pillar, etc), still stunned by Veigar stun (E) if he passes through it in pool-form, able to use summoner spells in pool-form (but not other spells), will not be healed from any source including the heal from Tranfusion (Q) as the heal from Tranfusion is a projectile.
• Tides of Blood (E) - Tides of Blood can stack up to 4 times. Each stack increasing healing and regeneration 4-8% costing only 30-70 HP on cast. Let's do some math. At lv5 Tides of Blood that's 8% increased healing per stack. With 4 stacks that 32% increased healing. A health potion increasing your health regeneration by 10 for 5 seconds ("Restores 150 health over 15 seconds."). Increase that by 32% -> 13.2 Hp/s for 5 seconds -> That results in 16HP. 16 HP for 70 HP? But that's not worth it is it? Well on top of the damage you've done and spell-vamp you've got, it can be worth it. For instance if you're alone farming top lane, it would be worth it to cast E once or twice between waves to keep your stacks if it means you will have 3-4 Stacks when you hit the entire next wave of minions (6 minions) with your E (assuming you have spell-vamp). Do not just mindlessly keep stacks because they increase healing if you don't plan on dealing any damage anytime soon because it costs more to keep the stacks. However, late-game 70 HP on your 3K+ HP isn't much and won't really matter all that much so just keep this in mind for early to mid game when you don't have as much HP and the cost could be detrimental Also note that the range indicator is just ever-so smaller than the actual range. Another note: Tides of Blood hits Stealthed and Enemies in Shrouded areas that you cannot see (such as a bush or around a corner).
• Hemoplague (R) - Vladimir is an Area of Effect (AoE) damage master. He excels at killing groups or entire teams. Why? Because of this little piece of his ultimate right here: "increases the damage they take from all sources by 12% for 5 seconds". If you're not using your ultimate in a fight first, you're missing out on a 12% damage amplification to every target you hit with your AoE Spells. That can result in up to 60% extra damage if you hit the entire enemy team. And that's from all sources. If you aren't initiating with your ultimate and doing your combo, you're not getting the most out of Vladimir. After all, this is why we have W and Hourglass is it not? We can initiate a fight and destroy the enemy team AND SURVIVE! Also note that the damage amplification applies to its own damage and there is no cast-time for this spell. The damage amplification applies to ALL forms of damage EXCEPT true damage. Interestingly, the damage amplification can increase the damage from item actives such as Deathfire Grasp. Lastly, casting your ultimate on a recalling enemy will not prevent them from backing as it only applies a debuff initially then explodes later.

I originally started this answer wanting to update the item mentions since they were out to date, so people finding this post would benefit. Additionally I ended up throwing a bunch of tips that came to mind (from experience). It's a bit off-topic but I really just want to spread my experience with Vladimir to others. I'd really like to seem more Vladimirs, Dianas, Swains, out there. There isn't enough!!