current levels sometimes in excess of 400 kA, temperatures to 50,000 degrees F., and speeds approaching one third the speed of light
These are massive numbers, but lightning protection systems are designed to draw the lightning away from the building or structure that they are protecting. Lightning protection systems can be simply thought of as lightning rods connected to the ground via cabling (downconductor).
The NOAA specification for lightning protection requires that lightning rods be at least 0.5in (13mm) in diameter. The downconductor is a similar size copper cable (4/0 AWG or 12mm). The allowable amperage for this type of wire is only about 250A for constant current. I realize that this is more of a heat limit rather than a instantaneous current capacity limit.
From this paper on lightning protection (page 28):
Positive feedback on the operation of a lightning protection system is seldom documented and most often not even noticed. Only in some rare cases can it be documented that a lightning protection system has been struck if it works properly and there is no damage. There is sometimes evidence at the strike termination point which can be noted during a careful inspection, but it is seldom cost effective for the owner of a lightning protection system to obtain the expertise necessary to conduct such a careful inspection.
How can a seemingly small 0.5in (13mm) piece of metal handle a lightning strike with little or no visible damage much less without being completely destroyed?