Have you followed the directions in the Owners Manuel to operate the left or right standing lights? [Note: The standing lamps discharge the battery. Avoid using the standing lamps for longer periods of time; otherwise, you may no longer be able to start the engine.] If a malfunction results with standing lights being "on," it may explain your previous battery problem. Also, try turning the standing lights "off" by selecting low beam on the headlight switch, ignition "on" and turn signal "off," the reverse of turning the standing lights "on." Your BMW dealer should be able to fix the lights by resetting the light control computer or trouble shoot the malfunction to the light switch, turn signal switch or lighting control module. Removing the side light bulbs will save the battery until you get to your dealer.
We picked up a Z4 on Christmas Eve and it appears some light operations have to be set by the dealer for individual preferences. Our dealer has set previous BMWs' lighting for our individual preferences.
May you have a Happy New Year with your Z4.