At the creation of this document Landing Pages plugin does not support featured images. None of our free or premium templates make use of the featured image so we do not include it.
That does not mean it cannot be used when building custom landing pages. You will know when it is relevant to your project.
To enable featured image support for Landing Pages please add this line of code to your theme’s functions.php file:
add_post_type_support( 'landing-page', 'thumbnail' );