You just have to buffer the last line you read and output it only after editing (if it needs to be edited):

#!/bin/perl -w
use strict;

my $last_line='';

while( <DATA>)
  { chomp;
    if( m{\bedit\b})
      { # edit to taste
        $last_line .= ' # edited';
      }
    print $last_line, "\n"; 
    $last_line= $_;         # buffer the line
  }
print $last_line, "\n";

__DATA__
***********************
word1  word2
word4  word3
word4  word5  word6
word7  word8  word9 edit
word10 word11
word12 word13 edit
************************
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Note that this way you only have 2 lines in memory at all time, which can be useful if you are processing a hige file.