Add info to row of table Data

I have a table wp_lb_family_group which has the following columns id, person_id, sibling_id, father_id, mother_id, family_id

Currently when a new family is created the person_id and family_id are automatically entered into the table successfully.

However at a later stage when a new family member is created I wish to enter their person_id as a sibling, father or mother in the sibling_id, father_id, mother_id columns of this table.

This is where I have hit a brick wall

(I am only trying to place the father_id at this stage. I have not added any code to determine whether the person is the mother, father or sibling. I will do this once I know how to put the info into the table)

The code I have at this stage is:

<?php
 require_once('../../../wp-config.php');
 // Get values from form
	$person=$_POST['person'];
	$family_type=$_POST['family_type'];
	$id=$_POST['id'];
	$first_name=$_POST['first_name'];
    $family_name=$_POST['family_name'];
    $date_of_birth=$_POST['date_of_birth'];
    $date_of_death=$_POST['date_of_death'];

?>
<!--I am only echoing the following variables to ensure they have been passed succesfuly. This will be removed at a later date-->

<?php echo $person;?>
<br />
<?php echo $family_type;?>
<br />
<?php echo $id;?>
<br />
<?php echo $first_name;?>
<br />
<?php echo $family_name;?>
<br />
<?php echo $date_of_birth;?>
<br />
<?php echo $date_of_death;?>

<?php 

global $wpdb;

$table_name = $wpdb->prefix . "lb_person";

$wpdb->insert($table_name,array('first_name'=>$_POST['first_name'], 'family_name'=>$_POST['family_name'], 'date_of_birth'=>$_POST['date_of_birth'], 'date_of_death'=>$_POST['date_of_death']));

$strSql = 'select last_insert_id() as lastId';
$result = mysql_query($strSql);
while($row = @mysql_fetch_assoc($result)){
$lastid = $row['lastId'];
}

$family_id = $wpdb->get_var( "SELECT family_id FROM wp_lb_family_group" );

<!--I am only echoing the following variables to ensure they have been passed succesffuly. This will be removed at a later date-->

echo "<p>Family  ID{$family_id }</p>";

$table_name = $wpdb->prefix . "lb_family_group";

$wpdb->insert($table_name,array('person_id'=>$lastid, 'family_id'=>$family_id));

Up to here everything works successfully.

The information is added to the lb_person table and the person_id and family_id are added to the lb_family_group table.

It is when I try to add the new family member to the father_id column that I am having problems.

I have tried the code with no effect:

$wpdb->update( $table_name, array( 'father_id' => $lastid), array( 'person_id' => $id), array( '%d'), array( '%d' ));
  ?>

Any assistance would be appreciated.