I have a 2000 L300 (LS2).
The compressor is getting no voltage.
I ran 12 volts from the battery to the compressor and it worked fine.
I then removed the relay and jumped the relay. The compressor worked fine.
I then bought 2 new relays. No power with the relay plugged in.

What is it about the relay that I don't understand?

There are safety switches in the relay circuit that prevent the compressor from running under certain conditions. They are:

1) No refrigerent in the lines (low pressure)
2) Compressor discharge pressure too high (no cooling to high pressure gas, or system improperly charged)
3) System thinks the engine is under very heavy load (passing gear, or pulling trailer uphill).
4) A/C switch is defective