As I understand it, Grant and Lincoln had spoken of the forthcoming inevitable defeat of Lee's army. If I recall rightly, he asked Lincoln about terms; to which Lincoln responded "Let'em up easy."
Lincoln wanted peace after the war, and as little residual hatred as possible. Grant knew that and therefore gave terms to Lee that he felt would help introduce the type of peace that Lincoln wanted. The economic destruction of the south, its catastrophic losses among white manhood, and loss of their slaves meant that the south was no threat for a long time to come. The north had every reason to be magnanimous, and nothing to lose by letting the disarmed ANV leave on parole.
I think that, civil war or not, we were still one people in most ways. By treating the surrendering rebels as countrymen rather than as national enemies, Grant did one of the greatest services that anybody has ever rendered to the nation.