I have a 55-plate LS430 which I know and love - been having issues with one of the keys recently, so in case this helps anyone here, I'll explain my history - it might work for you:
I have two keys - the "used" one, and the "spare" (hardly used), not sure which one is the true master key, if any is a true master key. All main dealer servicing from new etc as it's a complex car.
All was working fine until I sent it to my quite frankly, useless local Lexus dealer who did "something" whilst changing the remote battery for me at their discretion (trying to be kind), and gave me a broken remote key back. Keyless worked fine, physically putting the key into the ignition worked fine, blade worked fine (obviously), but I couldn't use the three remote buttons.
Symptoms were:
Key fob remote buttons wouldn't work - LED light in the key would flash sometimes. Remote key battery CR2032 fine and replaced myself.
What I know about this car LS430:
The key can unlock it 4 ways:
Blade
Keyless
Physical Presence in the ignition
Remote buttons
Spent ages worrying about reprogramming/paring the remote buttons with the car, and it changes by model year, other helpful posts on here say things like open/close door X times, do this, do that - never had to do any of this in the end - doesn't mean those posts are wrong, just that they didn't apply in my case.
Frustratingly, Lexus themselves, who "broke" it, have been very disowning of the problem, no feedback questionnaire offered, and have just outright refused to even look into this.
Here's what I did to fix it - turns out that the main car battery under the bonnet was knackered (only just found out yesterday), I replaced the battery.
Car booted up as usual after a flat battery - progress bar on dash etc.
I got in my car yesterday, and I know things about my LS through experience with it. Inserted the key in the dash and started the car, with the "other" key (good, all working), so the LS "trusts" that the good key is good and known to it. I kept the "bad key" well out of range all the time in the very back of my house, so no communications from bad-key-to-car.
I let the engine idle for a few minutes on the good key, just briefly moved the car back and forth so it'd think I'd driven it, hopefully strengthening the "trust bond" between the two - might be unnecessary, but who knows.
I got the "bad" key out of the back of the house, went to the LS, switched the engine off and removed the good key. I pressed buttons on the bad key (the LED was flashing 3 times), put the new key into the ignition, I know the car can programme its own keys. Started the engine, let it idle for a few minutes, hoping that this might somehow fix it... and it did!
Now both keys work fine.
So, in summary, here is what I did:
Replaced bad main car battery under the bonnet, let the car "boot up" etc for a while.
Started the car with the perfectly working key in the dash.
Waited, drove back-and-forth.
Whilst running, brought the old bad key out of the back of the house.
Switched the engine off via the good key in the dash.
Pressed some buttons on the old bad key to "wake it up" making the LED flash.
With both keys "with me" still sat in the car, I inserted the old bad key into the LS dash, started her up, and let her run for a while (2 mins) on the old bad key - my idea being, the car would "talk" to the old bad key, and "sort itself out", which it did.
Switched all off - all working perfectly fine now, I have two good keys again.
When I got the LS back in 2018 and had a bad battery, I've had similar issues but never this specific situation with only the "bad key" remote buttons only failing.
Best luck with your LS430s - they're truly a car like no other. 210,000-ish miles by the way, still smooth and silent as ever.