Using Meta Query when values are stored in an array

I'm trying to retrieve only those posts that have a value set in the meta data for a post. WP says to use the meta_query and pass an array with the key, value, and compare (optional). The problem is that the theme designer is storing the key and value in another array. Is there a way to retrieve this with WP_Query?

Failing that, how does one retrieve multiple posts by ID with WP_Query? I've my code currently is:

$recommendations_query = new WP_Query($recommendations_args);

I've also tried: