In order to unlock your LG Optimus L9 II (LG D605), You need to purchase a unlock code or ask it from your carrier.
When you get the unlock code, follow below instruction to unlock your device
1) From Your Phone Dialer, Dial “2945#*605#”
2) You will get the SIM Unlock Menu as below:
3) Tap SIM/USIM Unlock to input the Unlock code
Wish this helps!