This was something I came up with ages ago. Don't know if it'll play nice with current LWP or not, but it should get you started.

package MyHTTP; 
use base qw(LWP::Protocol::http); 

sub _new_socket { 
    my($self, $host, $port, $timeout) = @_;

    local($^W) = 0;  # IO::Socket::INET can be noisy
    my @args = (PeerAddr => $host,
                PeerPort => $port,
                Proto    => 'tcp',
                Timeout  => $timeout,
               );
    push @args, LocalAddr => $ENV{LWP_LOCAL_ADDR}
        if exists $ENV{LWP_LOCAL_ADDR};

    my $sock = IO::Socket::INET->new( @args );

    unless ($sock) {
        # IO::Socket::INET leaves additional error messages in $@
        $@ =~ s/^.*?: //;
        die "Can't connect to $host:$port ($@)";
    }
    $sock;
}

LWP::Protocol::implementor( 'http', 'MyHTTP' );

package main;

use LWP::Simple qw( getprint );

getprint( shift || 'http://localhost/' );

exit 0;

__END__
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