According to the log the SSL handshake itself succeeded: 
DEBUG: .../IO/Socket/SSL.pm:676: Net::SSLeay::connect -> 1
DEBUG: .../IO/Socket/SSL.pm:731: ssl handshake done
Which means the error must be at the HTTP layer. Check if the same URL is accessible with a browser, curl, wget ... - it can be that the server restricts access to specific user agents.

In reply to Re: Help with LWP & SSL 500 Internal response error by noxxi
in thread Help with LWP & SSL 500 Internal response error by dcsastry

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