Works for me.

plackup -e'sub{[200,[],[]]}'
starts a dummy Web server at localhost:5000. It doesn't proxy, it doesn't even do anything useful, but that's not important, the point is that it logs some output when it receives a request.

http_proxy=http://localhost:5000 no_proxy=perlmonks.org perl -mLWP::UserAgent -e'my $ua = LWP::UserAgent->new; $ua->env_proxy; $ua->get("http://example.net")'
gives error output from the dummy proxy - the LWP client tries to talk through the proxy.

http_proxy=http://localhost:5000 no_proxy=perlmonks.org perl -mLWP::UserAgent -e'my $ua = LWP::UserAgent->new; $ua->env_proxy; $ua->get("http://perlmonks.org/index.pl?node_id=1022784")'
gives no output from the dummy proxy - it is by-passed.