When Fields Are Not Displayed in the Order You Set in the Record Selection Screen of the Lookup Settings

If the field specified as "Key Field" is not listed in the "Fields Shown in Lookup Picker" section, that "Key Field" is displayed in the left most column of the record selection screen.

If you want to display the "Key Field" in any column other than the left most column, you need to list the field specified as "Key Field" in the "Fields Shown in Lookup Picker" section, and then set the display order.