Is it permissible to make use of a lab coat taken from the parent company, given the uncertainty of whether it was authorized by the company's management?

These clothes belong to the company, and the head of the department is not permitted to dispose of them except with the company's permission. If you know, or it is highly probable in your estimation, that she acted with permission and gave you the clothing, then there is no sin upon you in taking it. However, if you know, or it is highly probable in your estimation, that she was not authorized, then it is not permissible for you to take the uniform and you are obligated to return it.