There can be several reasons a DVD/CD drive will not eject the disc tray. The common causes are:
The disc was in use, but the program using the disc crashed. In this situation, in rare circumstances, the disc will be held indefinitely. Disconnect the drive from the computer, then manually power the drive back on. The exact way to manually power on a LaCie DVD drive varies from model to model, but there will either be a switch on the back, or a button on the front.
NOTE: On models with a blue button on the front, the button must be pressed harder than it appears would be necessary.
Once the drive is powered on again, press the eject button. The tray will eject. The drive can be reconnected to the computer after the disc has been removed.
The disc may be physically stuck. On the front of all DVD drives is a small hole. This is a way to manually eject the tray. Find a small object capable of fitting in that hole (like a paper clip or pin.) Inside is a small lever that is connected to the tray. Pressing it will open the drive slightly. The drive can be opened the rest of the way by pulling on the tray.