I tend to think LTT's persona & voice in Rand's head were real, but eventually integrated into Rand.

I think if Rand were really insane, he couldn't suddenly become sane, or? But if the explanation for Rand having LTT in his mind is that it was basically provided by the Wheel/Pattern, it makes sense that it can vanish, if Rand doesn't need it anymore (likely similar to other devices like ta'veren, Mat's dices or the swirling colors).