Do you think they will drop Lee at any point?
There is a whole lot of alumni opposition to that move. But W&L has made moves in the past that were incredibly unpopular with the alumni such as going coed and removing the Confederate Flag from the main floor of Lee Chapel. Certainly I don't think it will happen any time soon. I even go back and forth on the idea and I understand the problem it causes. W&L is the least diverse of the top liberal arts schools in this country, and it's not even close. And that affects the rankings and, if you buy into diversity as a benefit as I do, it affects the quality of the experience. As a small example, there are 2, count them 2, black football players. Last year there was 1. It's a huge image problem.
On the other hand, the side Lee chose in the Civil War had little to do with the benefits he brought to the school after the war. He instituted the single sanction honor code, the speaking tradition, he built Lee House, started the first Journalism school in the South, defined a W&L Gentleman (yes, it's a thing and yes it predates our coed integration by over 100 years!), and it's possible he saved a school that was teetering on the brink after losing so many students to the war itself. Did he support some bad things while at W&L as well? Certainly in the context of today he did when looking at the historical record. Though the school had racial issues before his Presidency as well including owning slaves.
W&L's racial past is checkered. The name Lee attached to the school is both a source of pride and a millstone around its neck. I am capable of appreciating Lee's contributions to the school while still understanding he fought on the morally wrong side of a war. But that kind of complexity is not so easy to explain to people all around.
I do not know if Lee's name will always adorn the school, nor do I know if I want it to. But I suspect it will not be going anywhere any time soon.