In the consumer market, the LC III was sold as the Performa 450. It's identical except for the sticker on the front of the case, and some accessories that came bundled with it.
LC III+ (still an 030, but faster) was sold as Performa 460, 466, 467
One step further, an 040 Mac LC was sold by several names. LC 475, Performa 475, 476, Quadra 605
It would appear that the IIe card will work in ALL of these. So maybe you can widen your search a bit if you don't mind the label saying "Performa XYZ" instead of LC III. I personally would prefer non-performa versions... BUT you take what you can get with these old things.
LC III+ (still an 030, but faster) was sold as Performa 460, 466, 467
One step further, an 040 Mac LC was sold by several names. LC 475, Performa 475, 476, Quadra 605
It would appear that the IIe card will work in ALL of these. So maybe you can widen your search a bit if you don't mind the label saying "Performa XYZ" instead of LC III. I personally would prefer non-performa versions... BUT you take what you can get with these old things.