See the Proxy attributes setting of LWP::UserAgent.

But from my experience, wanting/requiring a network connection just for running your module self tests will bring you lots of bogus failures for little gain. If you need the live connection to download additional data, consider packaging the additional data with your distribution instead - that way, users will always have a Known Good point of reference when they download a distribution of your module.

No changes to LWP required. You can get LWP::Simple to export the underlying LWP::UserAgent object. Once you have that you simply set the proxy option if the environment dictates. Just patch your module like this and it should work:

use LWP::Simple qw( get $ua );

$ua->proxy( ['http'], $ENV{HTTP_PROXY} ) if exists $ENV{HTTP_PROXY};
[download]

LWP::Simple is documented to call $ua->env_proxy, which fetches proxy information from the environment as documented in LWP::UserAgent.

It seems the env variable should be named http_proxy, not HTTP_PROXY.

On systems with case insensitive environment variables there exists a 
+name clash between the CGI environment variables and the HTTP_PROXY e
+nvironment variable normally picked up by env_proxy(). Because of thi
+s HTTP_PROXY is not honored for CGI scripts. The CGI_HTTP_PROXY envir
+onment variable can be used instead.

2001-03-14   Gisle Aas <gisle@ActiveState.com>

    Release 5.51

    SECURITY FIX: If LWP::UserAgent::env_proxy is called in a CGI
    environment, the case-insensitivity when looking for "http_proxy"
    permits "HTTP_PROXY" to be found, but this can be trivially set by
+ the
    web client using the "Proxy:" header.  The fix applied is that
    $ENV{HTTP_PROXY} is not longer honored for CGI scripts.
    The CGI_HTTP_PROXY environment variable can be used instead.
    Problem reported by Randal L. Schwartz.

sub env_proxy {
    my ($self) = @_;
    my($k,$v);
    while(($k, $v) = each %ENV) {
    if ($ENV{REQUEST_METHOD}) {
        # Need to be careful when called in the CGI environment, as
        # the HTTP_PROXY variable is under control of that other guy.
        next if $k =~ /^HTTP_/;
        $k = "HTTP_PROXY" if $k eq "CGI_HTTP_PROXY";
    }
    $k = lc($k);
    next unless $k =~ /^(.*)_proxy$/;
    $k = $1;
    if ($k eq 'no') {
        $self->no_proxy(split(/\s*,\s*/, $v));
    }
    else {
        $self->proxy($k, $v);
    }
    }
}
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use Net::SSL (); # From Crypt-SSLeay
use LWP::UserAgent;
$Net::HTTPS::SSL_SOCKET_CLASS = "Net::SSL"; # Force use of Net::SSL
$ENV{HTTPS_PROXY} = 'http://98.142.214.160:443';
$ENV{PERL_LWP_SSL_VERIFY_HOSTNAME} = 0;

my $ua = LWP::UserAgent->new();
my $req = HTTP::Request->new('GET','https://twitter.com');
my $res = $ua->request($req);
print $res->status_line;
[download]

Thank you so much for posting this. I was able to fix http://docs.aws.amazon.com/AWSEC2/latest/UserGuide/mon-scripts.html perl script when running behind a proxy.