I wasn't able to make it change the height even with

sub change_height {
    my ($widget, $height) = @_;
    print "Configuring $widget\n";
    eval { $widget->configure(-height => $height) };
    for my $subwidget ($widget->Subwidget) {
        change_height($subwidget, $height) if $subwidget;
    }
}
         
 $mw->Button(-text => 'Change Height',
       -font => $myFont,
       -command => sub { change_height($lb, 5); }, 
       )->pack();
[download]

I have no idea what to try next.

Looks like the trick is to manually add the scrollbars rather than using the Scrolled method. Problem solved (i think).

use strict;
use warnings;

use Tk qw(MainLoop); 

 my $mw = MainWindow->new(-title => " Listbox Height-Change Test");
 my $myFont = "{Lucida Fax} 12 bold";
 my $lb;
 
 $mw->Button(-text => 'Change Height',
       -font => $myFont,
       -command => sub { $lb->configure(-height=>5); }, 
       )->pack();         

  my @items = ("thing1", "THing2", "THING3");

  my $scrollbar = $mw->Scrollbar( ); 
 
  $lb = $mw->Listbox( 
             -yscrollcommand => ['set' => $scrollbar],
           -font => $myFont, 
           -background => 'darkblue',
           -foreground => 'white',
           -height => 15,
           -width => 28,
           -borderwidth => 1, 
           -relief => 'solid',
          );
 
    $scrollbar->configure(-command => ['yview' => $lb]);
    $scrollbar->pack(-side => 'right', -fill => 'y');
    $lb->pack();

 $lb->delete(0,'end');

 my $num = 0;
 $lb->insert('end', sprintf("%3d. $_\n", ++$num)) for (@items);
 
 MainLoop();
[download]

Apparently the Scrolled method creates a frame into which the listbox and scrollbar widgets are placed. I'm guessing that the frame somehow gets in the way of changing the listbox dimensions.

choroba's observation that a plain listbox could be modified inspired me to investigate further, leading to the solution I mentioned above. So thanks, choroba!