Modified pre-order tree traversal - order children by score

Question

So I have been able to output the data how I want except now I want to be able to rearrange it depending on the score of individual items. So right now I output something like this:

<ol>
 Item1
    <ol>
     subitem1A
        <ol>
         subsubitem1A
        </ol>
    </ol>
    <ol>
     subitem1B
    </ol>
</ol>
<ol>
 Item2
</ol>

I get that by putting the left and right values in an array and iterating through it. If it is a left value, it puts out <ol>item and if it is right it closes it with </ol>

Using the example above, what I want to do is if Item2 has a better score than Item1, Item2 will be first and Item1 with all its children will be after it. If subitem1B has a better score than subitem1A, subitem1B will be before subitem1A and all its children.

I'm not sure if I would have to do something with the DB query or something before running the loop that puts all the html in a variable for output, but I was thinking along the lines if I had the output somehow I could check for any <ol> that are direct children of the parent <ol>. So if I look at subitem1A and see its parent is Item1 then look for any <ol> who has parent Item1, check the score, and then order accordingly. I don't know if that is possible but it was my thought process.

edit - Adding more info as requested.

I do this query:

$sql = "SELECT * FROM table WHERE uCId = '$uCId' AND lft BETWEEN 2 AND '$max' ORDER BY lft ASC";
$result = mysql_query($sql);

Then:

$ol = array();
$html = "";
while ($row = mysql_fetch_array($result)) {          
        $ol[$row['lft']] = array('type'=>'open',
                                    'text'=>$row['text']
                                    //and more stuff like score, date, etc 
                                    );
        $ol[$row['rgt']]  = array('type'=>'close');
    }
$olCount = count($ol);
for ($d=2; $d<=$olCount; $d++) {
        if ($ol[$d]['type'] == 'open') {
            $html.= '<ol>various html'.$ol[$d]['text'].'various html';
                    }else{
                          $html .= '</ol>';
                    }

Basically I just left out some html which would just make things harder to read. The score can be placed anywhere it would need to be. the id for the <ol> could be the score or anything. Whatever would work.