Options when a disk does not unmount
Summary:
"Eject Failed" appears when attempting to unmount a drive.
There can be a variety of causes for this behavior. A clue about the origin is in the error message that appears. If the wording is: "The disk could not be unmounted. Make sure that all applications and files are closed on this disk." The cause is likely an open program, a file transfer, or an additional user on the machine using the disk.
If the wording "Resource Busy" is added to the error, close all open programs, and try again. If the message continues to appear, reboot the computer. There is usually a crashed program that can not be closed, or a cabling/power supply problem. Determining the origin can be done by using the Terminal program (located in Applications --> Utilities.)
Type the command:
lsof /Volumes/drive
Where the command says "drive", put the name of the LaCie drive that will not eject. In the example below, the drive is called "LaCie".

The listing underneath the word "COMMAND" shows the program occupying the drive. In this case, it's the "mds" process (Spotlight indexing) that is causing the problem. Usually, an Internet search will find the program responsible for the problematic command causing the error message.