So, both of my LSes are HID now, but till recently the 04 was halogen.
All gen II, halogen or HID, keep the low beams on with the high beams. No extra relays are used for this. Just the electronic drivers inside the FEM.
The 06 (HIDs from new) does have an extra relay added for the HIDs. Where as the halogens have the +12V wire always hot (while the car is awake) and the ground wire switched on and off to turn the low beam on and off, on the HID ones the relay changes this around so that the ground wire is always grounded, and the +12V wire is switched on and off to turn the low beam on and off.
I understand why they did this. They wanted the HID ballast to always be grounded. However, it was unnecessary. The factory HID headlights work just fine with the factory halogen wiring. You don't have to change anything, just cut the keying tab off of the connector on the HID headlight.
Also note that the reflectors are different on the HID headlights than on the halogen headlights. That's the other reason that you can't just put a HID bulb in a halogen headlight assembly.