Not the whole eletrical wiring swap. Besides the fog housing, you need the bulb holder and the connectors. Cut the old connectors from your existing harness off, splice on the "new" connectors, plug in, well done.
OP, you'll want to order two connectors from Toyota/Lexus: 90980-11156
The electrical probes they require are harder to identify by P/N but if you have made a habit of keeping random old unused Lexus electrical bits you can probably find the right ones to cannibalize. The only thing you'll be missing is the factory rubber seals on the OEM wires/probes.