The fact that it simpy, stopped makes it sound like your battery died. If you do need to program the remote though I found these instructions on clublexus.com. It was in the first gen section but they mention it may work on a 2nd gen.
Sit in the driver's seat and lock all the doors.
Unlock and open the driver's door.
Insert the key into the ignition and remove it (don't turn it...just remove it).
Using the MANUAL lock switch on the driver's door, lock and unlock the door 5 times.
Close the door.
Open the door.
Lock and unlock the driver's door 5 times (I'm almost certain you use the MANUAL lock switch again, but if this sequence fails to work, try again with the power switch).
Insert the key into the ignition and turn it to the "ON" position.
Remove the key.
The driver's door will now lock and unlock itself one time.
Press and hold the "LOCK" button on the key fob for at least 1 second.
Close the driver's door.
Open the driver's door.
Press and hold the "LOCK" button on the key fob for at least one second.
Close the driver's door.
Press and hold the "LOCK" button on the key fob. The door will lock.
Press and hold the "LOCK" button on the key fob again. The door will unlock.