Do I need to authenticate my ereader device with the Odilo credential?

Yes, indeed.

The reason is that files downloaded through lending are ACSM files, which means they are encrypted and linked to the identifier of the user who made the loan.
 
Therefore, both Adobe Digital Editions (ADE) and the ereader must be authenticated with the same account used to make the loan. If not, the encrypted file detects possible unauthorized use and does not allow it to be opened, neither in ADE nor on the ereader.