When Lucius had changed tasks with his master, his intentions had been pure, and he had hoped that by doing this, not only would the injured Hermes have some time tomorrow recuperate, but he would be well hidden from Brava's detection.
Moreover, aside his selfless reasons, another thing that had pushed Lucius into offering to take Hermes's task was simply because he had expected it to go just as smooth as with the students when they were told they were in danger and that their best bet in terms of safety was with the Protectors.