No you can't - at least not with the out-of-the-box lookup fields. If you
have no other alternative, you can create your own custom field  type to do
this.As a developer, I would recommend learning how to create custom
field types - it saved my hide several times.
 
FYI - Under the covers, the listitem with the lookup stores the ID and
description of the lookup item (delimited by ;#)For example, it
would store 3;#ItemDescription.In this example, 3 is the ID value for the
lookup listitem and ItemDescription is the text display value for this listitem.

The way SharePoint stores this value allows you to change the descriptions in
the lookup list  without impacting the listitems that reference it.