How should I use drupal_lookup_path()?
That's not what drupal_get_path() is for; it's for getting the internal router path for a URL given a path alias, and vice versa. It also allows you to wipe aliases, but it's not a good way to try to get the current page's node ID.

What you're looking for is the arg() function, which simply splits the current router path (the value contained in $_GET['q'], which for a node page will be, for example, node/1).

// With a router path of node/123
$entity_type = arg(0); // $entity_type is equal to 'node'

$nid = arg(1); // $nid is equal to 123