Pros:

Spells offer great utility
Can save herself with good use of ultimate
Glacial Path gives unique escape and initiation potential
Can initiate well and has good ganking potential
Built in High damage + CC on 3 of her Spells
Can be a massive damage/invulnerability threat in teamfights with Ult+Zhonyas Usage


Cons:

Ring of Frost could put you out of position trying to use it.
Long base cooldowns on most spells
Very low range compared to most AP mages
Really relies on teamplays, if you go in and the team doesn't follow you got a problem.

Playing teamfights almost always depends on the state of the game. If your carries are stronger, you can easily sit back, poke and peel for them. However, if they have carries with longer range, you'll clearly have to hard engage on them using Glacial Claw, Ring of Frost and your ultimate likely on yourself so that your allies can catch up to do damage while still surviving. This is a game of awareness so having a strong sense of how the game has flowed up until the teamfight phase is very important. If you've been roaming in the course of the game and have shut down someone specific to the point that they're easily killed in one rotation, feel free to do it. However, you do have to weight it against the idea that you're letting a few of the enemy carries go unharassed if you focus on one target.

Lissandra actually has a lot of mana problems, so be sure to fully utilize her passive when possible. Once you have a blue buff, which you should be getting as the mid laner, things change a lot and she can easily wave clear with one Ice Shard and a Glacial Path at around level 9. You can even just fire it straight into the wave when they're grouping near eachother. Be advised about using your Glacial Claw to farm however, if you get ganked after using it you'll most likely have to flash.

Lissandra is definitely one of the more interesting AP champions released as she has relatively low ranges and her ultimate ability winds up forcing you to make a choice. Should you use it as a Zhonya-like ability to survive and put yourself in the center of the enemies? Or should you use it on an enemy carry to stifle their damage and hopefully assassinate them? The answer tends to rely on the state of the game and how it flowed. If their carries are immensely fed, usually you want to assassinate, but don't take that to be an end-all statement, if a tank comes out of positioned, they might easily be a free kill if stunned for 1.5 seconds. Even assuming for their tank having tenacity, you never really know how it will play out until you do it.