I did find a workaround, so I am not in a dire need of help anymore. I am however curious if this is a fault or not (and if I can use LWP differently and get it to work). I added following line of code to get it work: 
delete $ENV{https_proxy};

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In reply to Re: LWP https problem with no_proxy by dian
in thread LWP https problem with no_proxy by dian

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