One way to do this (though not the easiest way) is to create a custom field type that extends the SPFieldLookup class. The SharePoint field editor for Lookup fields purposefully hides column types that are not supported by Lookup fields, but you can create a field editor for your custom field type that displays them.
However, I created the Lookup column, which used to point to the Name column in the document library, and it probably doesn't work as you expected. Although the value stored in the search column is valid, it does not display correctly in the List view or in the View Properties form.
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