use strict;
use warnings;
use LWP;
use IO::Handle;
use Fatal qw( open close );

my $url = 'https://........';
my filename = 'file2send.txt';
my $LINES_PER_CHUNK = 100;
open my $fh, '<', $filename;

sub sendthis {

    my @buf;
    my $linesread = 0;

    if ($fh->isopened) {
        while (my $line = <$fh>) {
            $linesread++;
            push(@buf, $line);
            if ($linesread == $LINES_PER_CHUNK) {
                return join('', @buf);
            }
        }
        close $fh;
        return join('', @buf);
    }

    return '';    
}

eval {
    my $headers = HTTP::Headers->new();
    $headers->header('Content-Type' => 'text/plain; charset=utf-8');
    $headers->header('Content-Length' => -s $file2send);
    my $request = HTTP::Request->new('POST', $url, $headers);
    $request->protocol('HTTP/1.1');
    my $browser = LWP::UserAgent->new();
    my $response = $browser->request($request, \&sendthis);
    my $gotthis = $response->content();
    print $gotthis;
};
if ($@) {
    # handle error !
}
[download]

So does this mean that the content-length header value is no longer used?

I can't tell from the LWP docs if it handles that for you, but you can still set it yourself, for example with my $length = -s $filename; and then adding the appropriate header.

Regarding your code, I read the docs slightly differently:

    my $request = HTTP::Request->new('POST', $url, $headers);
    $request->protocol('HTTP/1.1');
    my $browser = LWP::UserAgent->new();
    my $response = $browser->request($request, \&sendthis);
[download]

That is, you pass the callback to the LWP->request method, not the HTTP::Request constructor.

Thanks for the response.
I made the changes you suggested above.
Now if I could just get the client to give me a url so I can test....

Check out LWP/Protocol/http.pm
  When request is called here, your coderef is in $arg

sub request {
  my($self, $request, $proxy, $arg, $size, $timeout) = @_;
 ...
    my $content_ref = $request->content_ref;
    $content_ref = $$content_ref if ref($$content_ref);
....
        if (ref($content_ref) eq 'CODE') {
            my $buf = &$content_ref();
...

http.pm doesn't look at $arg as a code ref.
Instead it looks at $content_ref.
But if $content_ref was a code ref, then you'll get a run time error.

It'll never work !  This feature is totally broken.