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WARNING:
1- I nor XDA will not take any responsibility if your phone is damage/bricked/exploded\melt.
2- By rooting your phone, LG Singapore will consider you warranty is voided as per their LAME T & C.
3- Kindly charge your phone to 100%.

Rooting instruction:
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1. Install the USB driver needed to have ADB access to the phone, you can download it from here:

LGUnitedMobileDriver_S4981MAN32AP22_ML_WHQL_Ver_3. 2.exe
http://www.megaupload.com/?d=M8OF7XGT

2. Connect your phone, enable USB debugging (Settings->Applications->Development)

3. Run SuperOneClick
Download here > http://forum.xda-developers.com/attachment.php?attachmentid=624175&d=1307984755

a- Open SuperOneClick 1.9
b- Select psneuter
c- Hit root
d- Check Superuser app

No reboots or shell root required.

Su is permanent, withstands a reboot

5. Run the test in the end...and you will have it, you got root access on your 2.2.1 LG Optimus 2X device