With the help of ROM Manager application you can easily upgrade your LG Optimus 2X (LGP 990) with ICS 4.0.4 custom ROM.
For this you will have to first ROOT your device. To know how to root your LG Optimus 2X click here. Then install a free ROM Manager application available in Googly Play market.
Now download the custom ROM that you want to install/apply. Copy the custom ROM to your internal memory of LG Optimus 2X (LGP 990), you can even copy the ROM to external SD card as well. Now follow below mentioned steps to apply the custom ROM.
1. Launch the ROM Manager application, you will see the UI as below:
2. Click OK. Firstly you should backup your current ROM. You can have backup in two forms with Data and only ROM. You should take backup in both the form so that you can at least return to old ROM if something goes wrong.
3. Once you have backup of your current ROM. Now launch the ROM Manager again. Now select install ROM from SD card option.
4.Before you install new ROM you should wipe the cache and data partition depending upon compatibility with your current partition. Ideally flashing data and cache partition is good option.
Now selected ROM will get updated.
Some of the custom ROM's can be downloaded from below links :