Mazda Rotary engines used two injectors for years. One injector, the primary fed fuel all of the time. The secondary injector (the ones that were easy to see) only fed fuel under load, and when the intake runner control system was activated.
The Lexus system uses a typical intake runner injector, and the second injector is a direct injection system ( direct into the combustion chamber). This system makes use of a "stratified charge" for improved performance and emission standards.
One thing that never seems considered strongly enough is exactly how a technician is supposed to analyze a problem when a problem with a system like this finally occurs. I can easily envision individual cylinders suffering a fuel density missfire and only under specific engine load conditions. Which could mean, no way for the tech to re-create the conditions in the bay, and nothing but intuition to rely on for figuring out the problem with a customers vehicle. Sure some will say on-board diagnostics will show us what cylinder is miss firing and when, but truly almost everything else about the failure will be completely unknown. That amounts to too many variables that can only be worked through in lab type settings, where time isn't a factor. Meanwhile a technician is expected to diagnose the problem in a flat period of time, and then repair the circuit or change a part and always be correct the first time. That's a standard that if put to the test, NO-ONE could ever completely live up to.