#!/usr/bin/perl 

 my $inFile = "input file";
 my $outFile = "output file";
    open IN, "< $inFile";
    open OUT, ">> $outFile";
    
 my @not_sorted = <IN>;
 print OUT "|CSED Form|OrderNumber|Date|Total Documents|Total Pages|\n
+";
        @sorted = sort { lc($a) cmp lc($b) } @not_sorted; # alphabetic
+al sort
        my $a = 0;
        while ($lstxt = pop @sorted)
        {
                    $field[0] = $lstxt;
     $field[0] = substr $lstxt, 1, 3;
        $field[0] = $form;
        if ($form eq "M729")
            {
            print OUT "$lstxt";
            $a++;
            }
            else {
            print OUT "There were $a Monthly 729 runs\n";
            }
            $a = 0;
        if ($form eq "M737")
            {
            print OUT "$lstxt";
            $a++;
            }
            else{
            print OUT "there were $a Monthly 737 runs\n";
            }
            $a = 0;
        if ($form eq "Q569")
            {
            print OUT "$lstxt";
            }
            else{
            print OUT "there were $a Quarterly 569 runs\n";
            }

        }
 close OUT;
 close IN;
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warnings would have pointed you to a bug in your code: you never assign a value to $form.

Other suggestions:

• Use strict too (see use strict and warnings).
• Only use $a inside sort. Outside of your sort, change $a to $i or $count.
• perltidy can clean up your indentation.
• Show the output you expect.