Does the LS also have the red immobiliser light to the right of the steering wheel?
I know the GS does, when you insert the key you have, if the light goes out instantly = master transponder (you can program away with this) if the light stays of for just a about 1 second, it is the valet transponder, no amount of door locking pedal dancing will work to program in a spare.
I have bought a spare fob on fleabay and managed to program it in, plenty of guides around to tell you how to do it.