The Lucene index file format doesn't support document updating. Documents should be removed and re-added to the index to effectively update them.
Zend_Search_Lucene::delete() method operates with an internal
index document id. It can be retrieved from a query hit by 'id' property:
<?php
$removePath = ...;
$hits = $index->find('path:' . $removePath);
foreach ($hits as $hit) {
$index->delete($hit->id);
}