Yes, TD will lighten the color. I use a modest amount of TD to lighten soap that otherwise discolors to a dark tan. I don't weigh the amount of TD so I can't tell you an exact dosage unfortuantely. I don't add so much TD that the soap loses its translucency or becomes brittle or chalky. The result I get is a beige which is fine for my purposes.
I think there's a practical limit to how much TD can do. If you're hoping to get a light tan using a fragrance that normally discolors to dark brown, that might be expecting a lot.