the node is replaced by a blank line.

The node wasn't replaced with anything. You started with

< i t e m 1 / > LF < i t e m 2 / > LF < i t e m 3 / > LF
[download]

If you delete the second element, you get

< i t e m 1 / > LF LF < i t e m 3 / > LF
[download]

Nothing is added in its place.

You want to delete the leading newline of node that follows if it's a text node.

use strict;
use warnings;
use open ':std', ':locale';

use XML::LibXML qw( XML_TEXT_NODE );

sub remove_newline_that_follows {
   my ($node) = @_;
   my $next_node = $node->nextSibling()
      or return;
   $next_node->nodeType() == XML_TEXT_NODE
      or return;
   my $text = $next_node->data();
   $text eq ""
      and return remove_newline_that_follows($next_node);
   $text =~ s/^\n//
      and $next_node->setData($text);
}

sub remove_node {
   my ($node) = @_;
   $node->parentNode()->removeChild($node);
}


my $doc = XML::LibXML->load_xml( string => <<'__EOI__' );
<root>
<item1/>
<item2/>
<item3/>
</root>
__EOI__

my $root = $doc->documentElement();

my ($node) = $root->findnodes('//item2') or die;
remove_newline_that_follows($node);
remove_node($node);

print $root->toString();
[download]

---

Update: Tested and fixed the broken XPath (by replacing it). I was using the following (marked as untested):

my ($next_node) = $node->findnodes(
      'following-sibling::*[ position()=1 and text() ]')
   or return;
[download]

The correct XPath is

my ($next_node) = $node->findnodes(
      'following-sibling::node()[ position()=1 and self::text() ]')
   or return;
[download]

Of course, what I used instead is much clearer (and surely faster).

my $next_node = $node->nextSibling()
   or return;
$next_node->nodeType() == XML_TEXT_NODE
   or return;
[download]