my $statement = qq(
           INSERT INTO dickens VALUES ($word, $Line{$word})
        );
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No, don't do that. Use placeholders instead:

my $sth = $dbh->prepare('INSERT INTO dickens VALUES(?, ?)');

# and then, as often as you want:
$sth->execute($line, $count);
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I guess the database looks something like this:

   CREATE TABLE dickens (
           word VARCHAR(30),
           line INTEGER,
   );
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If that's the case, you can't store multiple line numbers in one row. In that case you have to make multiple rows with the same word, or change the database layout.

foreach $word ( @theseWords ) {
   my @lines = split m/ ,/, $Line{$word};
   for (@lines){ 
      $sth->execute($word, $_);
   }
}
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Of course it's better to store the line numbers as arrays in the first place.