im not sure why GD is involved, but for the calls using LWP::UserAgent i have a few suggestions. Lets assume you code looks like

 
my $ua = new LWP::UserAgent(); 
my $req = new HTTP::Request (GET => $uri);        
my $request = $ua->request ($req);
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have you inspected $request->content and $request->status_line for further info like

500 Can't connect to no.such.server.in.my.lan:80 (Bad hostname)
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That may help you identify what is going on.

ssl problems can also case a 500. if you change the line to

my $ua=LWP::UserAgent->new(ssl_opts => { verify_hostname => 0 });
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and it starts working it means you probably have outdated certificates. rather than to continue to skip ssl verification there are modules to update. Mozilla::CA IO::Socket::SSL Net::SSLeay come to mind.

if those dont seem to identify the problem add this

Use Data::Dumper; 
print Dumper ($request);
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That will dump the entire request hash, and inspecting it may provide further insight

one more thought. There may be some sort of blocking base on the agent. If you change the line to

  my $ua = new LWP::UserAgent(agent =>"myagent");
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and it starts working someone is filtering lwp. another agent you could try is something like

  my $ua = new LWP::UserAgent(agent =>"Mozilla/5.0 (Windows NT 5.1; rv
+:51.0) Gecko/20100101 Firefox/51.0");
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