Use item_lookup_field for DELETE methods

Existing code uses lookup to recover document. Once we've found the
"original" document we don't need lookup anymore and we can use
"original" document ID_FIELD.
Using lookup[ID_FIELD] forces to use just the ID_FIELD on path.

This change would be consistent with GET and PATCH methods where
changing item_lookup_field let items to be recovered/updated with other
fields than _id (or ID_FIELD for global configuration)