With the exception of Corki, Ezreal, and Urgot, every AD carry pretty much follows one of two "cookie cutter" builds. The below are simplified for the purpose of this post.

boots-> 1-2 dorans blades -> Blood thirster -> Phantom Dancer -OR-
boots-> 1-2 dorans blades -> Infinity Edge -> Phantom Dancer

For the Infinity Edge rush, Last Whisper has been mathematically proven to be superior as your third damage item when compared to picking up a Blood thirster. I'm not concerned with this.

However, If opting for the early Blood thirster, should Last Whisper still be purchased as your third item? I've never seen the math concerning an early BT build. Most AD Carries I see go for infinity edge 3rd, but it just takes way too long to build at that point and Bruisers/Initiators are running around armor stacked. Without the LW you're not going to tickle a bruiser to death before they kill you.

I'm going to test this out later but I'd like everyone's opinion on this until then. Thanks.

1) Don't rush LifeSteal (BT or ExCa) Infinity Edge is far superior, try to build it ASAP, with a simple Vamp Sceptre/Dorans for lane sustain...
2) Never buy Blood Thirster if you have IE/PD... Buy ExCa instead... It has great synergy with IE, you lose no damage (Due to Crit chance and Damage) or sustain compared to BT, but gain utility...
3) Last Whisper is NOT superior to Black Cleaver until your target has 170 Armour... If you take cost into account, this value is instead 120ish...

The money you save from buying ExCa instead of BT will allow you to buy BC instead of LW...

ExCa + BC is better than BT + LW

Unless you're having to hit 2+ targets with over 150 armor, it's not worth getting LW over other items like PD, IE. BT is questionable.

Eh, black cleaver has been mathmatically proven to be more effective than last whisper if your a smart ad carry (i.e. not ****ing targeting the bruiser or tank.) Just felt like pointing that out.

Basically... If you're GOOD at playing AD carry and you're able to consistantly get yourself into a position where you're able to attack high value, low armour targets...
ExCa + BC will give you better damage output than BT + LW...

If you're bad at positioning or they have a composition which genuinely doesn't allow you to target low armour targets first in a team fight (For example, if they ahve a sticky, gap-closing Bruiser and/or tank) you might be forced to do as much damage to high armour targets, while you wait for an opening to switch to a low armour target...

If you're attacking a tank, LW will help more...
If you're attacking who you SHOULD be attacking, if you're enemies let you... BC is better...

BC also benefits a team who is good at focusing one target...
The increased DPS of your Bruiser/Tank/Jungler/Auto-attacking support who is waiting on CD's should not be under-estimated...

A co-ordinated team, with good positioning... Playing against a less co-ordinated team who has bad positioning... Use BC...

So, as with every item, other than IE and PD, your choice should depend on how the game is going...

Also, If you're good at last hitting, you shouldn't be running Flat AD runes, and instead grab a few ArPen runes... They offer nearly the same early damage out-put, scale better with time... And decrease the effectiveness of LW, but don't alter the effectiveness of BC negatively...

I believe that the reason Pro's justify using LW more than BC is because even though they have the best AD carries in the world, the other team still has good positioning, which means the carry's only option is to target a high armour target...
BC lets you capitilize on your enemies mistakes, buying LW means you're assuming they won't screw up majorly...
Which in competitive play doesn't happen often...

LW is the safer option, BC is the superior option...

You have a lot to consider. LW is better against enemies with lots of armor, where cleaver is better for enemies with a little less armor, since its stacks remove flat armor. If you buy LW vs someone with 50 armor, you'll penetrate 40% of their armor, thus their effective armor is 30. However, with 3 stacks of cleaver, you've reduced their armor to 5. However, if you're attacking someone with 200 armor, a LW will get rid of 80 armor, whereas a cleaver with max stacks removes only 45.

Next question is how many cleaver stacks can you get? Are you kiting enemies by an autoattack, move, autoattack, move method? Or are you able to play offensively and attack non-stop? If you are forced to play in the former, consider a LW instead because you may have trouble getting max cleaver stacks.