Is it permissible to take the lodging allowance designated for external work in the event of not going for external work, but by direction of the administration, and what is the ruling of Islamic law on that, knowing that not taking it will lead to the loss of the lodging balance?

The issue lies in the rightful entitlement to the money. If the employee is entitled to the mentioned amount by virtue of labor law, then it is permissible to take it, even if they have not yet departed, as long as they are making themselves available to depart. However, if the manager favors them with company money, then it is not permissible for the employee to take the money, because the manager is an agent and a trustee over the company's funds, and it is not permissible for them to favor employees with its money except with explicit or customary permission.