Also, for converting Curl command lines to LWP (or HTTP::Tiny), see HTTP::Request::FromCurl, or its live site at https://corion.net/curl2lwp.psgi.

The Curl command

curl -d '{"some":"json"}' destination
[download]

gives

#!perl
use strict;
use warnings;

use LWP::UserAgent;

my $ua = LWP::UserAgent->new( 'send_te' => '0' );
my $r  = HTTP::Request->new(
    'POST' => 'http://destination/',
    [
        'Accept'         => '*/*',
        'Host'           => 'destination:80',
        'User-Agent'     => 'curl/7.55.1',
        'Content-Length' => '15',
        'Content-Type'   => 'application/x-www-form-urlencoded',
    ],
    "{\x22some\x22:\x22json\x22}"
);
my $res = $ua->request( $r, );


__END__

Created from curl command line
curl -d '{"some":"json"}' destination
[download]

This should give the OP a decent starting point.