How to query post ids liked by the Author

Your query would be something like:

$post_ids = $wpdb->get_col( "SELECT DISTINCT post_id FROM {$wpdb->prefix}wti_like_post WHERE user_id = {$author->ID}" );

Then you can pass that array of post IDs as the post__in argument of WP_Query:

$args = array(
    'posts_per_page' => -1,
    'post__in' => $post_ids
);