A representation mustvbe given to the higher authorities and a writ petition must be immediately fiked in the high court so that the court may pass appropriate orders regarding the noc.

Regards 

You can submit your resignation from LIC . Serve your notice period 

2) you won’t need your NOC from your employer for appearing for interview 

3) don’t suppress any material facts 

Alternative to  NOC is resignation from service 

Issuing NoC is well within the right of management. Without NoC it will be illegal to sit in govt.  Exam. 

You have to take a decision based on  prevailing law.

There are two ways one you don't disclose that you are in job can apply for the SSC examination the other where is to file a mandamus writ petition in High Court in this regard to get the direction from the high court to LIC to issue no objection certificate principal LIC cannot hold no objection certificate if there is no certain reason available for this.

You need to approach office of labour commisionner or court for the same as they need to provide you noc. If it's urgent you can directly move under writ petition to high court

Apply through proper channel then at the time of interview ask for the NOC they will be force to do so, don't delay your application , apply now.

Approach tribunal for direction to release NOC.

Dear 

If your employer is not providing the NOC then you should file resignation from current job and go for main exams.

You should not hide any facts from PCS commission.

Other option is to file a case of mandatory injunction against your employer in court for issuance of NOC for mains Exam. 

Yes that is what i told you. They cannot deny you noc.if they do they have to pass a reasoned and speaking order. Even thatvorder can be challenged. Therefore act accordingly.

Regards 

Ps you can resign...the easiest way out.

Did you apply for NOC in writing mentioning the said reasons?

If so, did the LIC management refuse to issue the same in writing ?

Did you make a representation to the top management in writing after this refusal and also did you inform your trade union  about this?

After exhausting all the above remedies you may plan to proceed legally on this.

You may follow the procedures as suggested in my previous post and after getting no fruitful result you may plan to initiate steps to procure the same legally.

NOC for appearing in the examination is essential hence you may have to initiate  legal steps if you dont get any response from management