Runes:
The main rune that is going to be used is , it gives great sustain, stacks alot of base damage and scales great from early game to mid-late game. And Lee Sin only needs one combo to stack up to max.

The second rune rune that really awesome on Lee Sin is Electrocute, because it give som ekstra burst damage that helps Lee Sin become the assassin he shines to be. his kit i amazing to proc the rune with already from level 1, just Q - Q - auto attack.

on the assassin set you can switch out Relentless Hunter with Ultimate Hunter so your ultimate is up for a gank more often an the faster you have your ultimate the faster can you make some plays.

Skills:
So what skill you want to max first depends on what you want to be doing through the game. Assassin Lee, would go Q-max, because 1. it is very usefull at ganking 2. it procs electricute.

you want to max your E first you u want to be more like a lane bruiser, because the ability is more likely to hit the target, its a great lane clear and becomes a monster with a life steal item and some conqouror.

your W is going to be used as an escape early game, and as a catch up later in the game, also very great at saving teammates in the middle of their 1 vs 1.

Items:
Sanguine Blade is great rushing if u have an okay early game, it gives an amazing lead.
or else for assassin rush duskblade, and for bruiser rush to finish the Tiamat.

Note: Sanguine Blade also works awesome on bruiser lee.

counters:
its annoying to play against a tank early game...

easier matchups:
some ranged matchups is easier to play against as assassin lee.

Mordekaiser is put under counter matchup because his passive makes it hard for Lee Sin to engage and Lee Sin is not tanky enough to stand up with Mordekaiser long enough.

but matches against Darius, Ryze, Vayne, Irelia and so on should be easier.