Intercept invalid email during lost_password

Try this:

add_action( 'lost_password', 'wpse316932_redirect_wrong_email' );
function wpse316932_redirect_wrong_email() {
    global $errors;

    if ( $error = $errors->get_error_code() ) {
        wp_safe_redirect( 'lost-password/?error=" . $error );
    } else {
        wp_safe_redirect( "lost-password/' );
    }    
}

This is utilizing the lost_password action hook that fires right before the lost password form.

You were experiencing this because WP will only redirect you to the url you specified in redirect_to input field when there is no errors. If it finds errors in processing the form (which is the obvious case here), it simply continues with rendering the form on the wp-login.php page. By using this action you can hook into this procedure right before that.