LWP comes with lwp-request program, very useful

> lwp-request -USexd -m get http://cpan.org/
LWP::UserAgent::new: ()
LWP::UserAgent::request: ()
LWP::UserAgent::send_request: GET http://cpan.org/
LWP::UserAgent::_need_proxy: Not proxied
LWP::Protocol::http::request: ()
LWP::Protocol::collect: read 782 bytes
LWP::Protocol::collect: read 1880 bytes
LWP::Protocol::collect: read 1256 bytes
LWP::UserAgent::request: Simple response: OK
GET http://cpan.org/
User-Agent: lwp-request/5.810

GET http://cpan.org/ --> 200 OK
Connection: close
Date: Thu, 17 Jul 2008 03:20:43 GMT
Accept-Ranges: bytes
ETag: "a9dc69-f4e-487d100c"
Server: Apache/1.3.37
Content-Length: 3918
Content-Type: text/html
Content-Type: text/html
Last-Modified: Tue, 15 Jul 2008 21:01:00 GMT
Client-Date: Thu, 17 Jul 2008 03:24:58 GMT
Client-Peer: 66.39.76.93:80
Client-Response-Num: 1
Link: <mailto:cpan@perl.org>; rev="made"
Title: CPAN
[download]

You can see request headers (option -U). If you examine lwp-request source, you'll see

    if ($options{'u'} || $options{'U'}) {
        my $url = $response->request->url->as_string;
        print "$method $url\n";
        print $response->request->headers_as_string, "\n" if $options{
+'U'};
    }
[download]

More details in HTTP::Response documentation.