Jamie, I have never read that Lee was a bitter man, or became one after the war as the venerable president of Washington-Lee Univ. Tempered by four long years of battle, I would think he would not be given to such melodramatic sentiments of little pragmatic value. Sounds more like something manufactured by the "Lost Cause" merchants for eager public consumption.
I never read that Lee was so blind-sided in his prognostications about what the enemy would do as to be completely surprised by the events following laying down the ANV's arms and going home. Nossir, the whole quote smacks of that safe, rear-echelon bellicosity that fat-cat politicians of both sides excelled in. It just doesn't seem authentic to Lee, the old warrior, who at that stage of the game was probably more concerned with mainstreaming the South back into the Union.
But if I had any disposable income left to gamble, I'd double down on the quote being fake, or at least not from Lee.