The admin notice “Your website is hosted using the LiteSpeed web server. Please consult this article if you have problems backing up.” means that your web hosting company uses the LiteSpeed webserver. LiteSpeed appears to have issues with all WordPress scheduled tasks that last more than a very short time – including all backup plugins.
You need to make changes to files .htaccess and wp-config.php which are located in the root folder on your FTP server:
1) .htaccess (add this line at the bottom):
RewriteRule .* - [E=noabort:1]
2) wp-config.php (add these values or replace old ones if they exist):
define('DISABLE_WP_CRON', true);
define('ALTERNATE_WP_CRON', true);