With the LED in parallel with the bulb as in ron's drqwing, it should come on whenever the outside bulb is energized, even if the outside bulb has burned out. If you put the LED in series with the bulb, then the bulb will not come on because the LED acts as a large series impedance that reduces the energy available to the bulb by 99%-ish.
What you haven't said is what you are trying to achieve. Do you want the LED to come on when the switch is in the on position? Or go off when the switch is in the on position? If that is all, I have to wonder why, but it doesn't affect the answer. If you want the LED to indicate whether or not the outside light has burned out, that is a very different wiring problem. In lieu of photos, how many wires are inside the switch box? What are the colors, pairings, and locations?
ak