You can install Joomla on your account from the automatic script installation system - Softaculous. Here is the way of installing Joomla from Softaculous:
Go to cPanel --> Softaculous. Pick the preferred version of Joomla from Portals/CMS and click on the Install tab.
For detailed instructions on how to install Joomla on your account, please check this tutorial.
You can also request the script to be installed on your account by SiteGround Technical Support Team. They would gladly assist you with the installation of any script/application that is compatible with your hosting account.
Log in to your hostlantern Customer Area --> Support tab --> Open a Support Ticket --> Script Installation
Joomla is a powerful software that is easy to work with once you have the right host to support you. Before you lose any more time with the wrong host, check out the SiteGround Joomla hosting offer.