Item Build

Starting Items

You want to start off with Boots + 3 Pots in almost every game. The only alternative really would be Boots + 2 wards+ Pot or Boots + 4 pots if you stay back in base and don't leash for your jungler or steal a jungle camp. 

Core Items

Why Mercury Treads?

You want Mercury Treads because you're a melee champion and therefore prone to the highest chance of being crowd controlled. You don't want to be stunned so long that you can't Safeguard(W) out of the fight or use Resonating Strike to stick to an enemy. Crowd control is a melee champion's biggest fear, and you mitigate magic damage as well as keep yourself moving with Mercury Treads.

Buying Order

After boots, I like to buy straight damage items, so if you have had a rather average game, you can look to get components of Brutalizer and plenty of pots / wards on your first buy back. Brutalizer is just too good after the Armor Pen changes to not buy every game on Lee Sin. After completing it, look towards buying another large damage item, generally Blood thirster and try to farm it out as much as possible. A Lee Sin with a Brutalizer/Blood Thirster mid game will be able to basically one shot any  enemy champion and you should look to capitalize on this strength through roaming/forcing skirmishes. 

Next, you need to get a GA because Lee Sin is very prone to being focused down and killed in fights, so having at least one tanky item, especially one that provides you with dual resists and a fall back plan incase you get CC'd to death is an exceptional choice. Of course, there are many iterations of builds that can work well, but in general a GA is always a safe choice. If you're against a very heavy AD team, consider a Randuin's to shut down those attack speed based champions. If you're against a heavy Magical damage team, you can throw in a Hexdrinker or even just a Negatron Cloak for the pure defensive stats. 

Finally, when lategame starts rolling around and you start to feel weaker as Lee Sin, you should get a Last Whisper because you should get this around the same time as most people complete their big armor items. Suddenly, you will start hitting like a truck again! And no need to feel as if your Brutalizer was a wasted purchase, due to the new armor penetration calculations. You can even eventually upgrade it into the new Black Cleaver, which is quite good on Lee Sin, among  other bruisers such as Riven/Wukong.

Endgame Items

These will be your items you shoot for at the end of the game. Here is the reasoning behind it:

Blood Thirster is a solid and effective damage item that scales well with Lee Sin's innate lifesteal and let's you chunk people for huge amounts with his combos. Guardian Angel is a must because of his innate weaknesses as a Melee Assassin and deals with the reality of the fact that he is easy to focus/burst down. 

Last Whisper will make sure your damage stays strong throughout the game, and is generally a great item for bruisers to have as it's relatively cheap and extremely effective. You don't want most of your damage negated when an enemy buys a 700g Chain Vest.

Black Cleaver is a natural upgrade from Brutalizer which you should have purchased to dominate early/mid game and is very nice when Lee Sin Combo's someone with Q+R+Q. Your last item ideally would provide damage and some further form of tankiness, which is why Maw of Malmortius is good. There are many choices for your last item but in general you probably won't be going wrong with Maw unless they really have no form of Burst Magic Damage, incase a Randuin's would completely shut down their damage output.