If Lexus do not take me up on the offer to investigate the fault I will be taking it apart myself.
However, I suspect that the radio unit was causing the drain, faulty diode, etc. By disconnecting the positive of the battery I suspect it found a path to discharge the stored charge frying the PSU or something more sensitive. It may be inrush current when the new battery is connected but any car audio designer should have protected against this reasonably well.
A battery saver or connecting the battery in parallel may have saved the head unit but I suspect I may have been back to the battery discharging if the head unit is at fault.
I'm not absolutely convinced that changing the battery causes the fault, more that it triggers the catastrophic failure that is waiting to happen because something has already failed. If it isn't that then all IS300H owners are sitting there with a potentially expensive failure waiting to happen.
As Rayaans said the batteries are expensive, you can't buy them in most usual stockists because of their unique size. I wish I had let the dealer do it and hopefully incure the cost of replacing the unit.