Since OSX Lion is a 64bit operating system the LaCie Safe Hard drives do not yet work with Lion as they use 32bit software to control them.
To get round this you need to boot your Mac running OSX Lion into 32bit mode. To do this you have to restart or boot your Mac while holding the ‘3’ and ‘2’ keys on your keyboard. You won’t hear a bing or chime to tell you you have done this successfully but trust me this works. The LaCie software jumps back into action.
If you want to return to 64bit mode for all your other apps and gaming just hold the ‘6’ and ‘4’ keys down while starting up your Mac.
Please leave a comment or share this with your friends if you find this has helped. Thanks.

YOU ARE AWSOME!
IT WORKS!
Thank you!
It worked for while, now it doesn’t work anymore. Perhaps because I also downloaded the newly upgraded SAFE Mobile software.
Thank you very much – brought back my Time Machine backup volume! (Still, I will replace the disk by an unencrypted one, since 32-bit mode is not an option forever.)