You did not initialize your cookie jar properly.

See LWP::UserAgent and HTTP::Cookies for how to specify the cookie jar.

Thanks for the answer, of course.

I looked in LWP::UserAgent previously and I still hope I can supply just a string with cookie itself, not cookies.lwp file. Basic question - is it possible?

In HTTP::Cookies is mentioned I should supply cookie from a file. Which I hoped to avoid...

As plan B, I will try to create lwp cookies. But it is Catch XXII, no knowledge of structure-> no cookie-> not functional connection-> no updated cookie, thus no connection. But that might be another question, I haven't searched for answer yet.

A cookie is just another header. A cookie jar is a collection of cookies that the browser can search by the page it is going to and select the right ones to send back

if you wanted to just supply a single cookie and not care about any cookies you get back you could try this

  my $ua=LWP::UserAgent->new(keep_alive=>1);
 my $getline='http://place.to.go.to/'; 
 my $req = new HTTP::Request (GET => $getline
                              ,HTTP::Headers->new('Cookie'=> 'JSESSION
+ID=F97AC6F5AD33D54D0C06F4CBF0230C43' )
                              );
  my $request = $ua->request ($req);
[download]

When i want to use a "stand alone" cookie-jar i do something like this

  my $cookie_jar_obj = HTTP::Cookies->new(ignore_discard=>1,hide_cooki
+e2=>1);
  my $ua=LWP::UserAgent->new(keep_alive=>1);
  $ua->cookie_jar( $cookie_jar_obj ); 
  $cookie_jar_obj->set_cookie(0, 'JSESSIONID', 'F97AC6F5AD33D54D0C06F4
+CBF0230C43'
                             , '/', 'place.to.go.to', 80
                             , '', '', 14400000, 0 
                             ); 
  $cookie_jar_obj->set_cookie(0, 'LoginUsername', 'Operator'
                             , '/', 'place.to.go.to', 80
                             , '', '', 14400000, 0 
                             ); 
  $cookie_jar_obj->set_cookie(0, "LoginPassword", 'Operator'
                             , '/', 'place.to.go.to', 80
                             , '', '', 14400000, 0 
                             ); 
$repeatme=1; 
while ($repeatme) { 
  my $getline='http://place.to.go.to/'; 
  my $req = new HTTP::Request (GET => $getline); 
  my $request = $ua->request ($req);
  if (some-test-for-done){ $repeatme=0;} 
  }
[download]

In both cases those are just cut and pastes from existing code and not tested as they appear here. YMMV

It feels strange to answer to myself. But here is an answer which describes the best my original problem.

Use cURL to retrieve original cookie? Then continue with cURL. If you plan to use LWP or JIRA::Client::Automated, like me, get cookie via this agent. See following code:

use LWP::UserAgent;
use HTTP::Request;
my $user = "JIRAusername";
my $password = "Lamepassword";
my $jira_url = "put_your_server_here";
my $ck=LWP::UserAgent->new( );
my $getline= $jira_url . '/jiraurl/rest/auth/1/session'; 
my $request = new HTTP::Request (GET => $getline, HTTP::Headers->new('
+Content_Type' => 'application/json') );
$request->authorization_basic($user, $password);
my $answer = $ck->request ($request);
my $cookie = $answer->header('Set-Cookie');
[download]

my $ua=LWP::UserAgent->new( keep_alive => 1 );
my $key = 'existing_issue_code'; #this is just for test. You can use a
+ny issue you get from web JIRA
$getline=$url . '/rest/api/latest/issue/' . $key;
$request = new HTTP::Request (GET => $getline, HTTP::Headers->new('Coo
+kie'=> $cookie ) );
$answer = $ua->request ($request);
[download]

I will spend some time by debugging of updated version of JIRA::Client::Automated and post it on CPAN later.