Oops, should’ve looked at the code more carefully earlier.
To resolve my problem, I changed the post_type that LCP was requesting to ‘any’ (see code below). I didn’t really do any debugging, so I’m not sure why LCP was behaving differently between posts and pages. My guess is that LCP determines the post_type from the current post/page you’re viewing (since I didn’t see any way to set post_type in the widget options).
I currently have LCP version 0.30.3. In include/CatList.php, I changed lines 53-55 from
if($this->lcp_not_empty('post_type')):
$args['post_type'] = $this->params['post_type'];
endif;
to $args['post_type'] = 'any';
Reference:
http://wordpress.org/support/topic/plugin-map-categories-to-pages-how-to-put-pages-list-in-widget-sidebar