As far as I understand, LWA stands for Leave Without Allowance. I also understand that this leave is granted when a Kerala Government employee who has not completed the probation period and who does not have sufficient leave in his/her account, applies for leave. It must be clearly understood that a Government employee on leave (any type of leave) remains a Government employee. So, to apply for another job (Government or private), he/she must apply through proper channel (i.e., he/she must intimate the current office).
In view of the above position, I would advise you to apply through proper channel and send an advance copy of your application for the new job. Please keep a copy of your application through proper channel. In case of your selection to the new job and if there is no reply from your present office, you can easily produce the copy of your application sent through proper channel. In that case, it would be taken as 'deemed approval' (the details and rule position is not required at this stage, but definitely there is such a provision).
Further, I would strongly advise you not to hide your present employment. If you abruptly leave the present job without following proper procedure, after getting selected for the new job, there is a real possibility of your being declared as 'bhagora' (deserter). In the present era of AADHAR, PAN Card and other computer-based Identity Cards, such risk must not be taken.
From my personal experience, I can assure you that applying through proper channel is not a very tough/complex task as it seems.
"If you are killed in action, you go to Heaven. If you win, you rule this Earth (as beautiful as Heaven). That is why, O son of Kunti, take a firm resolve and fight!"-- Shrimad Bhagwad Gita