zerg has many opening depending on location/match up.
My personal fav BO and style is the famous lurk/ling.
To use lurk/ling you have to have a constanly moving mouse and a good control of location hotkeys (f2 - f4) this will ensure that u are always constant scanning around the map; it will help on flanking units cause lurk/ling is for flanking not taking pure grounds head on. lurk/ling is very useful vs 2 rax terran tech bo, 2 gate zeal/archon/temp, it is not reccmmended vs zerg unless you switch to hydra/queen/lurk atfer early game.
There is many other zerg opening in LT, alot of people use a early expo because of a better and faster economy. To establish a good expo early on, you must make 1 sunken and 1 colony on the zerg expo when its done. don't make the colony a sunken until u see a force coming to you, if u don't make that a sunken you will save 50 mineral which is enough for drone. Atfer you took your expo and teched; depending on matchup you can go muta or lurk. Although some people in zvp go for early ultra/ling with fast amour upgrade, this tactic is very risky because u might get defeated half way to ultra.