Duplicated (non-trivial) code should be extracted into subroutines. For example:

Date_Cmp(
            _dateformat($_->get('hb_Local_date_lodged')),
            _dateformat($self->{date_str})
          )
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could become a function.

As a matter of personal taste, I'd turn

    exists $check{$_->qcs_job_name}
                 {$lodgement->{reference}}
                 {$_->qcs_sequence_no})
              && ($check{$_->qcs_job_name}
                 {$lodgement->{reference}}
                 {$_->qcs_sequence_no})
              && ($client_job_spoil
                 ->hb_Local_spoils == 0);
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into a function. When I encounter a "next if", I don't want to dwell on the logic of the test, but to simply note that a test exists.

Finally (and again, this is all just personal taste), consider changing

  $total_lodged 
    = $_->qcs_document_count() 
      - $client_job_spoil
        ->hb_Local_spoils;
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to

  $total_lodged = $_->qcs_document_count() - $client_job_spoil->hb_Loc
+al_spoils;
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It takes fewer lines and (if you align equal signs and operations) should be just as readable, if not more.