Based on OpenSSL changes in PHP 5.6, try this:
$arrContextOptions=array(
    "ssl"=>array(
        "verify_peer"=>false,
        "verify_peer_name"=>false,
    ),
);  
$response = file_get_contents("https://www.ladygaga.com/", false, stream_context_create($arrContextOptions));
echo $response;
Another option would be to use curl as such:
function file_get_contents_curl( $url ) {
  $ch = curl_init();
  curl_setopt( $ch, CURLOPT_AUTOREFERER, TRUE );
  curl_setopt( $ch, CURLOPT_HEADER, 0 );
  curl_setopt( $ch, CURLOPT_RETURNTRANSFER, 1 );
  curl_setopt( $ch, CURLOPT_URL, $url );
  curl_setopt( $ch, CURLOPT_FOLLOWLOCATION, TRUE );
  $data = curl_exec( $ch );
  curl_close( $ch );
  return $data;
}
$data = file_get_contents_curl("https://www.ladygaga.com");