I just looked at Youtube and they showed the LS430 brakes and they were doing the driver side and it definitely had the anti-rattle spring (I believe thats what it is technically called) in place, so whoever did your brakes last probably messed up....? I have worked on Toyotas that had a similar setup and it was identical on both sides as well.
I worked on one where I had to bend the center of the "spring" up about a quarter inch (relative to the ends), so that when installed it provided tension to the brake pad. Might be what you need to do here.
I haven't actually worked on an LS430 so I cant get too specific.
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