I suspect you'll have to use the callback to take chunks from LWP and feed them to your XML parser. You can use open to fork with a pipe to the child and feed the data through that. Here's a sketch:

my $pid = open my $child_fh, '|-'
die "Can't fork: $!" if ! defined $pid;
if ( $pid ) {
    # parent
    # feed LWP results into $child_fh
    close $child_fh;
}
else {
    # child
    # STDIN is the parent
    exit;
}
[download]