jquery & ajax sending data to php

First of all, your js is wrong, you are mixing the syntax of jQuery.post() and of jQuery.ajax()

You should use

jQuery.ajax({
  type: "POST",
  url: ajaxurl,
  data: { action: "lu_ajax", status: "enabled" },
  success: function( data ) {
    alert(data);
  }
});

or

jQuery.post(
  ajaxurl,
  { action: "lu_ajax", status: "enabled" },
  function(data) {
    alert(data);
  }
);

After that the ajaxurl js variable is available only in admin pages, not in frontend.

So the code above will work only in admin pages, but once you use add_action('wp_ajax_nopriv_lu_ajax', 'lu_ajax'); I think you want to use ajax in frontend, in this case you have to pass the ajax url to the script via wp_localize_script.

So if the js script in which reside the js code above is names ‘my_ajax.js’ and resides in the ‘js’ subfolder of your plugin, do something like this

add_action('wp_enqueue_scripts', function() {
  wp_enqueue_script('my-ajax', plugins_url('js/my_ajax.js', __FILE__) );
  wp_localize_script(
    'my-ajax',
    'myAjaxData',
     array( 'ajaxurl' => admin_url('admin-ajax.php') )
  );
});

Now the in the js code above replace ajaxurl with myAjaxData.ajaxurl