I am not going to create a big and difficult to read guide because I hate them...
I started playing Lissandra two days ago and I am still trying to find the perfect build for her!
II hope that you will find thsi guide useful :)

Lissandra’s magic twists the pure power of ice into something dark and terrible. With the force of her black ice, she does more than freeze – she impales and crushes those who oppose her. To the terrified denizens of the north, she is known only as "The Ice Witch". The truth is much more sinister: Lissandra is a corrupter of nature who plots to unleash an ice age on the world.
Centuries ago, Lissandra betrayed her tribe to evil creatures, known as the Frozen Watchers, in return for power. That was the last day that warm blood ran through her veins. With her corrupted tribesmen and the strength of the Watchers, she swept across the land like a terrible blizzard. As her empire spread, the world grew colder and ice choked the land. When the Watchers were defeated by ancient heroes, Lissandra did not lose faith and swore to prepare the world for their return.
Lissandra worked to purge all knowledge of the Watchers from the world. Using magic to take human form, she masqueraded as numerous seers and elders. Over the course of generations, she rewrote the stories of the Freljord, and so the history of its people changed. Today the fragmented retellings of the Watchers are seen as children’s tales. But this deception wasn't enough – Lissandra also needed an army.

She set her sights on the noble Frostguard tribe. Lissandra knew corrupting the Frostguard would take centuries, and so she launched her greatest deception. She murdered and stole the identity of the Frostguard leader. Then she slowly began to warp the tribe’s proud traditions. When her human form grew old, she faked her own death and then murdered her successor to steal her identity. With each generation, the Frostguard grew more insular, cruel and twisted. Today, the world still sees them as a noble and peaceful tribe that guards against evil creatures like the Ice Witch. In truth, they now serve the witch and long for the glorious return of the Watchers.

Pros:

Loads of damage
Great AOE
Low cooldown time
VERY high mobility and escape mechanisms
Nice passive
Great auto attack animation allowing you to farm easily

Cons:

VERY mana dependent and hungry
A bit squishy
Skill shot abilities

Every 18 seconds, Lissandra's next ability costs no mana. Cooldown reduction does not affect Iceborn, but the cooldown is reduced by 1 second whenever Lissandra is casting a AOE skill.

This passive is so helpful when harrasing at early game! If you use it wisely it can keep you full of mana and your enemy with lower HP!

Throws a spear of ice that travels in a line and shatters when it hits an enemy, dealing 75 / 220 / 245 / 180 / 215 (+65% of ability power) magic damage and slowing its Movement Speed for 1.5 seconds.

The Q! Unfortunately it doesn't have a big range but....! You can hit your enemy easily in front of CS. The icy blunt that she is throwing crashes in smaller pieces and does the job! Its cooldown time is mental!

Freezes an area around Lissandra, dealing 70 / 110 / 150 / 190 / 230 (+60% of ability power) magic damage to nearby enemies and rooting them for 1.1 / 1.2 / 1.3 / 1.4 / 1.5 seconds.

Awesome ability and good damage! It is perfect for escaping or chasing enemies. Also you can use it in case of a tower dive to root the enemy and kill him!

Casts a claw of ice that moves forward in a line, dealing 70 / 115 / 160 / 205 / 250 (+60% of ability power) magic damage to all enemies hit. Reactivating this ability transports Lissandra to the claw's current location.

This skill is magical! Its range is so OP! The cooldown is high so you must use it wisely.
It can be used to:
Jump between even the thickest walls on the game
Escape from enemies by: 1) confusing the enemies to the opposite direction 2) gain distance between you and the enemy.
This picture might be able to understand how loooooong it is:


Enemy Cast: Freezes target champion solid, dealing 150 / 300 / 450 (+70% of ability power) magic damage and stunning it for 1.5 seconds.

Self Cast: Lissandra encases herself in dark ice for 1.5 seconds, becoming untargetable and invulnerable but unable to take any actions. The Dark ice then spreads from Lissandra's target dealing 150 / 300 / 450 (+70% of ability power) magic damage to enemies. The ice lasts for 3 seconds and slows enemy Movement Speed by 20%.

Its cooldown is dissent and combined with the other skills it can guarantee you a kill! If you have purchase a Zonya's then you can use it to sustain your self during a fight and also use your ultimate to kill enemies!

For runes I select:

9 greater Mark of Magic Penetration
9 greater Seal of Armor
9 greater Glyph of Ability Power
3 greater Quintessences of ability Power

These runes are good against a 'regular mid' as I refer to them. These can be Mongana, Annie, Lux, Kassadin etc..

In the case of Kha or Zed I choose:

9 greater Mark of Magic Penetration
9 greater Seal of Armor
9 greater Glyph of Armor
3 greater Quintessences of ability Power


With this extra little armor you would be able to fight back against mainly AD mids

Rod of Ages:
+450 Health
+450 Mana
+60 Ability Power

Passive: Grants +20 Health, +20 Mana, and +2 Ability Power per stack (max +200 Health, +200 Mana, and +20 Ability Power). Grants 1 stack per minute (max 10 stacks).
UNIQUE Passive - Valor's Reward: Upon leveling up, restores 150 Health and 200 Mana over 8 seconds.

Sorcerer's Shoes:
+15 Magic Penetration

UNIQUE Passive - Enhanced Movement: +45 Movement Speed
(Magic Penetration: Magic damage is increased by ignoring an amount of the target's Magic Resist equal to Magic Penetration.)

(Unique Passives with the same name don't stack.)

Zhonya's Hourglass:
+120 Ability Power
+50 Armor

UNIQUE Active - Stasis: Champion becomes invulnerable and untargetable for 2.5 seconds, but is unable to move, attack, cast spells, or use items during this time (90 second cooldown).

Rabadon's Deathcap:
+120 Ability Power

UNIQUE Passive: Increases Ability Power by 30%.

Rylai's Crystal Scepter:]
+500 Health
+80 Ability Power

UNIQUE Passive: Dealing spell damage slows the target's Movement Speed by 35% for 1.5 seconds (15% for multi-target and damage-over-time spells).

Void Staff:
+70 Ability Power

UNIQUE Passive: Magic damage ignores 35% of the target's Magic Resist (applies before Magic Penetration).

Against enemy champions:
E+W+Q+R translates to: Move close to the enemy, root him, damage him, ulti him, kill him!

In a team fight:
Use your ulti wisely!!
Stun the fed champion or the adc to stop their ultimates or buy some time for your team-mates.

Against CS:
Q+E translates to: lower CS life and then root them and... poof! FARM!

Thanks for reading!