How can I disable W3 Total Cache Image Lazy Load for Specific Post Type?

This answer might be a bit too late but here goes: W3 Total Cache will skip lazy loading images that have class "no-lazy". This means that you can hook to the get_the_post_thumbnail() filter post_thumbnail_html and add the class to the image.

Here's an example:

/**
 * Disable W3 Total Cache lazy load for post type "post"
 *
 * @param string $html
 * @param int $post_id
 * @param int $image_id
 * @param string|int[] $size
 * @param string|array $attr
 */
function _post_thumbnail_html( $html, $post_id, $image_id, $size, $attr ){

    if( !empty( $html ) ){
        $post = get_post( $post_id );

        if( 'post' === $post->post_type ){
            if( isset( $attr['class'] ) ){
                $attr['class'] .= ' no-lazy';
            }else{
                if( !is_array( $attr ) ){
                    $attr = array();
                }

                $attr['class'] = 'no-lazy';
            }

            $html = wp_get_attachment_image( $image_id, $size, false, $attr );
        }

    }

    return $html;
}
add_filter( 'post_thumbnail_html', '_post_thumbnail_html', 10, 5 );

You can use this filter,

function ar_lazyload_deactivate() {
    if ( is_singular( 'posttype name' ) ) {
        add_filter( 'do_rocket_lazyload', '__return_false' );
    }
}
add_filter( 'wp', __NAMESPACE__ . '\ar_lazyload_deactivate' );