it depends on wheter your lcd has an inverter itself or not..
I'm assuming for this brand/size/make that the ivertor for the backlight is already implemented in your LCD
Part of...I need to feed 12V to inverter and inverter will light up LCD.
Is it correct?
Depends on how much power/current the inverter needs.. but most likely this will be 12v
your invertor will light up lcd by sending it's high voltage (~1000v) to the backlight-cathode (look out with this!).
Can you post pictures of your LCD to make sure that it has an invertor.. I'm assuming it has one. but i always could be wrong...