Hey.

This is how I usually play as Lee Sin. He's a really strong jungler that is able to pull of some amazing stuff with his really cool skills that have a very wide range of effects.

Sonic Wave: Lee Sin projects a discordant wave of sound to locate his enemies, dealing physical damage to the first enemy it encounters. If Sonic Wave hits, Lee Sin can cast Resonating Strike for the next 3 seconds.
Cost: 60 energy.
Resonating Strike: Lee Sin dashes to the enemy hit by Sonic Wave, dealing physical damage plus 10% of their missing health.
Cost: 40 energy.

Cooldown: 10 / 9 / 8 / 7 / 6 seconds.
Physical Damage: 60 / 90 / 120 / 150 / 180 (+1 per bonus attack damage).

[SW/RS]

Safeguard: Lee Sin rushes towards a target ally, shielding them both from damage. If a shield is broken, half the energy cost is returned. After using Safeguard, Lee Sin can cast Iron Will for the next 3 seconds.
Cooldown: 8 seconds
Cost: 60 energy.
Iron Will: Lee Sin's intense training allows him to thrive in battle. For 5 seconds, Lee Sin gains lifesteal, spell vamp, and armor.
Cost: 40 energy.

Shield Strength: 40 / 80 / 120 / 160 / 200 (+0.8 per ability power).
Spell Vamp & Lifesteal Bonus: 10 / 15 / 20 / 25 / 30 %.
Armor Bonus: 10 / 15 / 20 / 25 / 30 .

[SG/IW]

Tempest: Lee Sin smashes the ground sending out a shockwave that deals magic damage and reveals enemy units hit. If Tempest hits an enemy, Lee Sin can cast Cripple for the next 3 seconds.
Cooldown: 10 seconds.
Cost: 60 energy.
Cripple: Lee Sin cripples nearby enemies revealed by Tempest, reducing their movement and attack speed for 4 seconds. Movement and attack speed recover gradually over the duration.
Cost: 40 energy.

Magic Damage: 60 / 95 / 130 / 165 / 200 (+1 per bonus attack damage).
Slow: 30 / 37.5 / 45 / 52.5 / 60 %.

[TE/CR]

Active): Lee Sin performs a powerful roundhouse kick launching his target back, dealing physical damage to the target and any enemies they collide with. Enemies the target collides with are knocked into the air for a short duration.
No cost.

Cooldown: 90 / 75 / 60 seconds.
Physical Damage: 200 / 400 / 600 (+2 per bonus attack damage).

[DR]

I chose the ArP Marks to deal more dmg.
The dodge seals for his q(initiate), e(slow), r(kick to teammates) and then w(to get back to teammates) rota + help at jungling.
CDr since the energy doesnt run out as fast as it does on akali, shen or kennen and your w is going to save your life a ton of times if the cd get's off it in time.

The quints are something else.
Life is useful for the firstblood because you will have more health left after your jungle-route (Earlygame focus and we all know that an early game can decide very much, especially on Twisted Treeline)
Movespeed will help you always since you can basically choose merc treads with movement bonus 3 (Always helpful ex. chasing, fleeing etc.)
More ArP is also very helpful to deal more dmg, especially right after u get your Triforce. (Focus on Midgame)

The most important thing about jungling with Lee Sin is to use his passive right.

You will initiate with an autoattack then use w to shield yourself, 2 autoattacks and then again w to activate his passive again and to gain his extremely strong lifesteal. Afterwards e to use the lifesteal/sellvamp (whatever gains him the hp since it's a skill but is based on ad) of your w to get more hp back from the surrounding creeps, 2 autoattacks, depending on the situation you will press e again to activate your passive (enough energy left) if not, use q to get more lifesteal and use less energy.

Route:

If the enemy has a jungler or a strong counter like Eve or Rammus then your route will be like this:

Wraiths (smite the blue one), Golems(pot), Wolves(pot), Blue(pot), Red(smite)(pot),(pot) Gank

If the enemy ain't got a jungler or a strong counter your route will be:

Blue(blue), Wolves, Wraiths, depending on if smite is up Red or if not - Golems.

Fighting will depend on where the enemy is and if he's stronger than you. Use q + charge, autohitt, w, w, for lifesteal and then back. If he's weaker than you, you'll try to hit him with q at any chance to be able to initiate

(but always think about those things -> how much dmg will those minons and he give me?, is he able to stun me? where are his and where are my teammates?)

and slow with e and then standard jungling-rota (w,2 autoattacks, w, 2 autoattacks, q, 2 autoattacks, q, and so on.)

His core items are : Triforce, Mercury Treads and Wriggles.

His Triforce will pump your dmg up quite a bit and your red buff will do the rest. After that we need to get more hp to be more useful in ganks and to be able to focus their carry.

Warmogs + Atma's is a great combination to get really beefy and not lose too much dmg. Usually I get a banshees veil to be able to attack head on and slow everyone for my teammates and maybe even kick their dmg dealer away or even better to your teammates and then w to your teammates to get a very nice start-situation for your team.

This is where the game usually ends but sometimes it just dragges on and then I decide to get even more beefy since autoattacks are usually weak against lee sin as he'S got a as-debuff on his e but their casters still hurt you quite a bit. So I sell wriggles and get Nature Force for the MR and more movement speed which is just too awesome with Lee Sin.

His ultimate is really useful in ganks, solo fights and even escaping :]

Some examples of situations and how to use your ultimate

A big fight -> initiate with q, slow with e, kick carry/dd to your teammates and then jump with w to your teammates.

enemy is stronger but a teammate is coming -> initiate, w, w, e, e, r to your teammate

enemy is weak and u want to finish him off in a cool way -> dmg him until he's almost dead and then roundhouse kick to make him explode :D

you're getting ganked -> kick the first guy to his teammmates and jump with w to teammate or just run.

to get the enemies in a good position while runnig away - find a narrow path like at the 2 golems or just go to the next bush since they'll most likely run the shortest way and that is pretty much always a very thin line. Stand in brush, kick first one into teammates and run :]

So if there are any questions left, dont be shy to ask in the comments. I'm having a hangover right now so I just hope that I didnt forget to menton a lot of things.

I'll expand this guide every time I can.

Hf and gl with a really strong jungler that is a great Allrounder because he's so much fun to play since he's always able to do something that is useful for his or his teammates.