If you are open to alternatives this uses Mojo::DOM:

#!/usr/bin/perl

use strict;
use warnings;
use Mojo::DOM;

my $html = '<ul><li>1</li><li>2</li><li></li><li>4</li><li></li><li>si
+x</li>';

my $dom = Mojo::DOM->new( $html );

for ( $dom->find('li:empty')->each ){

    $_->remove();

}

print "$dom\n";
[download]

Update: output: <ul><li>1</li><li>2</li><li>4</li><li>six</li></ul>