opened my hood today to find all this white residue all over. Looks like something splashed. Unsure if it's coolant? Looks like that's the origin of it.
Do I need to replace my radiator? Or should I worry about the cap (before)?

The engine is running at standard temps, right at the halfway line. Nothing indicates it's overheating or anything like that

2002 Lexus LS430 with 116k. Not sure if it's worth noting I live in south florida, it's always excessively hot here

 

Not sure when this splash happened, but it's happened in the past week for sure. I didn't see any broken cables. I noticed that the coolant was almost empty, probably related to this. Cleaned the engine, refilled the coolant, took it for a long drive. So far all is good.

Will be replacing the coolant cap soon.

 

how does the grille and front of radiator look? Could this be splash from the road? The coolant dries to a crust with a slight pinkish tint which to my eye is not present in your pictures. It could be your radiator cap gasket failed when the system pressurized and that is what you are seeing so replacement of the cap is a good move to start with.

The road splash hypothesis would have more oomph if you have this white stuff present on the bottom of the belly pan aka splash guard. . . .

 

I had this on another car, it was a hairline crack in the radiator that gushed when it got hot.
clean it all off and check after every drive, to try and better pinpoint the origin (assuming it's not actually the radiator cap)

 

That's definitely coolant spray. You can do some CSI to find out where the spray came from. Most auto parts stores will loan you a cooling system pressure tester to help with diagnosis.