This is how I would have done what you tried in your code. As you can see, I kept Tk out of the worker thread.YMMV

#!/usr/bin/perl
use strict;
use Tk;
use threads;
use threads::shared;

my $data_out:shared = 0;
my $data_in:shared = 0;

threads->new( \&update_thread )->detach;
create_tk_window();

######################################################### 

sub update_thread {
    print "update_thread called...\n";
    while (1) {
          $data_in = 'thread-processing'.$data_out;
          sleep 1;
          }
    exit();
}


sub create_tk_window {
  my $mw = MainWindow->new(
        -background => '#dedede',
        -foreground => 'yellow',
        -title      => "FingerLick"
    );
    $mw->geometry("802x618");
    $mw->minsize( 802, 618 );
    $mw->maxsize( 802, 618 );

  my $sent_recvd_listbox = $mw->Scrolled('Listbox',
        -height     => 20,
        -width      => 60,
        -background => 'black',
        -foreground => 'yellow'
    )->pack( -side => 'bottom', -anchor => 's', -pady => 2 );

  my $server_list_listbox = $mw->Scrolled(
        "Listbox",
        -height     => 20,
        -width      => 60,
        -background => 'white',
        -foreground => 'black',
        -scrollbars => 'se',
    )->pack();

  $mw->repeat(1000, sub{
    $data_out++;
    $server_list_listbox->insert( 'end', "Sent $data_out " );
    $server_list_listbox->see('end');

    $sent_recvd_listbox->insert( 'end', "Recived $data_in" );
    $sent_recvd_listbox->see('end');
    });

MainLoop;
}
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