The correct answer is: persuade.
To persuade someone is to convince them to do something by using reasoning or argument. In this case, the manager is trying to convince his employees to return to work before he has to declare a lockout.
The other options are not as accurate. To motivate someone is to encourage them to do something by giving them a reason to do it. To encourage someone is to give them support or encouragement. To permit someone is to allow them to do something.
In this case, the manager is not trying to give his employees a reason to return to work, or to support them in their decision not to return to work. He is trying to convince them to return to work. Therefore, the best answer is persuade.