我的解决方案：

$data = array(
    array('id' => 1, 'parent_id' => null, 'name' => 'lorem ipsum'),
    array('id' => 2, 'parent_id' => 1, 'name' => 'lorem ipsum1'),
    array('id' => 3, 'parent_id' => 1, 'name' => 'lorem ipsum2'),
    array('id' => 4, 'parent_id' => 2, 'name' => 'lorem ipsum3'),
    array('id' => 5, 'parent_id' => 3, 'name' => 'lorem ipsum4'),
    array('id' => 6, 'parent_id' => null, 'name' => 'lorem ipsum5'),
);

$itemsByReference = array();

// Build array of item references:
foreach($data as $key => &$item) {
   $itemsByReference[$item['id']] = &$item;
   // Children array:
   $itemsByReference[$item['id']]['children'] = array();
   // Empty data class (so that json_encode adds "data: {}" ) 
   $itemsByReference[$item['id']]['data'] = new StdClass();
}

// Set items as children of the relevant parent item.
foreach($data as $key => &$item)
   if($item['parent_id'] && isset($itemsByReference[$item['parent_id']]))
      $itemsByReference [$item['parent_id']]['children'][] = &$item;

// Remove items that were added to parents elsewhere:
foreach($data as $key => &$item) {
   if($item['parent_id'] && isset($itemsByReference[$item['parent_id']]))
      unset($data[$key]);
}

// Encode:
$json = json_encode($data);