LaCie External Drive won't stop

My G4 iMac is only linked to a 250 GB LaCie d2-Triple external drive for monthly back-up.
Right now, I want to disconnect the LaCie drive, which is normally preceded by dragging drive icon to TRASH or by control/click/Eject.
Neither method works now, just get a warning message
"The operation could not be completed because the disk "LaCie disk" is in use.
But there does not seem to be any data transfer activity.
The activity light on LaCie is on but steady.
No sounds.
Process viewer shows Firefox 40 % and Finder 60%.
How can I force the LaCie to shutdown?
I am reluctant to just unplug it.

Is spotlight indexing the drive.

Using OS X 10.2.8 I do not have 'spotlight' - but you may be right that there is some indexing going on.
So I have now used
Finder/filename of LaCie/Info/Content Index/ Index Now
in the hope this will eventually bring things to a halt.

Try logging out and logging in again.

Logged out and then in again, then dragging LaCie icon to Trash worked as normal [ i.e. Eject ].

Many thanks - I was getting desperate!