I recall seeing a lot of white lithium-like greases used inside car doors, on window regulators/mechanisms, rods and linkages for door latches and locking parts.
I don't remember what the particular advantage/beneficial feature of white lithium grease is, and I'm too lazy to look it up, but I think it had one particular feature.
It gets used a lot, almost anywhere on cars.. door hinges, battery connectors, sheathed cables etc.
It doesn't seem to present any problems when it's used in enclosed spaces (light duty gear cases), but I've found lots of dried out white lithium inside vented equipment.. dried enough that it can't be wiped away for cleaning, it needs to be attacked with solvents or scraped away. It gets semi-solid like wax as it gets dried out.
Like I said earlier, I used to use it (fairly frequently) but I prefer many other types of greases over white lithium anymore.
One grease that I started using for certain applications like machine rack & pinion, drill press quill sliding surfaces and other gear-type applications, is a thick, non-silicone, synthetic gel-looking grease for brake caliper pins. It's really sticky, and continues to pull itself back into the pressure areas really well, whereas some greases just squish out to the sides of where they're needed.