How to Root LG Optimus 2X : http://www.lg-phones.org/how-to-root-lg-optimus-2x.html
What you need Before rooting your LG Optimus 2X:
1. You need to have a working USB connection between your computer and the LG Optimus 2X. One of the easiest way to setup working drivers in your computer for LG android devices is to install LG PC Suite. This software is usually shipped along with the device. If you don’t have it, you can download LG PC Suite and install it. After LG PC Suite installation, your computer and android device should be able to communicate with each other.
Alternatively, you can setup ADB in Windows PC for successful USB connection.
2. Download “SuperOneClick.zip” on to your computer and extract it’s contents.
How to root LG Optimus 2X Steps:
1. Put your LG Optimus 2X into “USB Debugging Mode”. To do it, go to “Applications”—> “Settings” –> “Applications” –> “Development” –> and check the box “USB debugging”.
2. Connect the LG Optimus 2X to your computer using USB Cable.
3. Open the download the extracted folder content “SuperOneClickv1.6.5-ShortFuse” and run the executable “SuperOneClick.exe”.
4. Click on “Root” button.
In few seconds, your LG Optimus 2X should get rooted! You now have full file system access and can now install apps that need root access for working.