Two responses:

First, consider Lee's feelings at the moment. He expressed frustration with the obligation to manage Arlington several times, and managing the Custis slaves was most of the problem. In his will Mr Custis left large bequests to his grandchildren, but debts of the estate (which Lee as executor had to settle) left no cash to pay them. Given a choice, Lee would have preferred to be with his regiment on the frontier, but felt duty-bound to honor his obligations. That meant paying the estate debts and funding the bequests by producing income from the Arlington plantation.

By all accounts, slaves at Arlington never had done hard work in their lives. It's understandable that they thought when Mr Custis died, freedom would follow immediately.

Hiring Norris and other slave out to earn money for the estate seems like a reasonable option. When the debts of the estate were paid, the slaves would be freed, as they eventually were. Meanwhile let somebody else manage them. Lee wouldn't have to check on them, try to get them to work and listen to their complaints. Plus, they could learn about daily labor, which would serve them well as free persons.

As for the whippings and the brine, I can easily understand Lee's feelings towards Norris and his friends. They were guilty of desertion from duty. I'd react exactly as Norris described. I'd have made sure they knew how angry I was, but have an overseer or constable carry out the punishment. I'd have promised more of the same if they ever ran away again.

Lee didn't usually pardon soldiers who ran away from his army. By the same token I wouldn't expect him to simply scold runaway slaves, warn them not to do it again and let them go with no other punishment.

Now to the question of 'Did This Really Happen?' Checking the Alexandria census for 1860, I found no one named Richard or Dick Williams, and no one named Williams who is a constable. It's interesting that there are many people named Williams on the Alexandria census who appear to be free blacks. I also find no one living in Alexandria named Gwin or anything similar. Surely some Lee researcher has checked this part of the story, but at the moment I have no evidence of either person mentioned in the Norris account. We also have nothing from Lee himself about this incident, which seems unusual to me.

Lee indicated earlier (1856) that he regarded slavery as a political and moral evil. But being confronted with a management problem involving slaves and forced to make a decision about punishment was another thing. In my opinion the Norris story sounds reasonable, but right now I have nothing to confirm the story as factual.