Yes, a user can define his own lookup provided he has at least create permission for the lookups in order to create a lookup. The user can refer to his permission by going to the profile and then clicking on permissions tab. The user has to click on 'Create Lookup' button in the lookup tab in the admin module.
The user can either manually add lookup values or has the liberty to download a template, fill it and re-upload it.
The new user created lookups are added in the portal specific lookups tab.
