BINGO!
Everything ok, the Lacie blue light stops flashing, the Mac sees it again via the Dashboard.
My beloved Volumes are now inside the folder /Share/Recovery
I miss two steps:
1) Move the volumes in the main path. I can do it via File Browser? Simply move the folders with a drag & drop?
2) the Lacie firmware is 2.2.3 which is the original one from the factory,
All it happenedI when have tried to do an upgrade to 2.2.12.2 from 2.2.9.3, From the one installed now, there are 9 updates!
You recommended to make the upgrade? :-)