From your question, it appears that the Army person, who was working as LDC, was working as a civilian in the army (and, not as uniformed person, it appears). This means that he was a Government servant working under the Central Government. It also appears that he died on duty, but not as a consequence of duty related risk such as an army jawan martyred while in action. Please correct me if I am wrong on facts.
In such a situation, usually he would be subject to the benefits which are available under the Central Civil Services (Pension) Rules, such as family pension, death gratuity, leave encashment, GPF payment, Insurance payment as per rules, etc. There may also be appointment on sympathetic grounds / compensatory job, subject to rules.
Labour Court will not have jurisdiction in the case of Central Government servants.
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