I just completed a test implementation of LightSpeed eCommerce using the latest version of Magento (1.7), hosted on Go Daddy.
Things went smoothly, although the documentation on the LightSpeed website is a little outdated: clearly Magento 1.7 fixed the issue described in the documentation, and some of the nomenclature in Magento menus is a little different.
Installing Magento 1.7 onto a shared hosting account on Go Daddy was easy as pie. Configuring LightSpeed to integrate with it was even easier. The hardest part of the installation is modifying the look and feel of the Magento store, but with the abundance of documentation, training material, and community, this isn’t hard to figure out.
The cost of hosting the Magento store on Go Daddy is extremely attractive. With an SSL certificate, it works out to about $75 (CA) per year. If you have some technical skill, and nerves, this is a good option.