Hi, unfortunately your old license won't work, the domain can be transfer, no problem with that, but since 6-months period has passed, you have lost your chance to get the latest version of LightMart. By the time you purchase LightMart (2015), the versions for both VM and Joomla were ancient, so I believe you wouldn't want to install those ancient versions to your server for security reason.
To support the latest version of Joomla + Virtuemart, you can purchase
MaterialMart -- a VM template only (gets integrated to your current plain joomla template and styles only VM related pages)
www.flexiblewebdesign.com/Virtuemart-Templates/MaterialMart
SportMart -- All in one Joomla Virtuemart Template (both Joomla and Virtuemart Template, just like LightMart)
www.flexiblewebdesign.com/Joomla-Virtuemart-Templates/SportMart
Regards.