Lab Services does do something somewhat similar, but only for a VM, not for an Azure environment. I'm not aware of any common templates for setting up a sandbox- how you set up your environment is going to be very specific to what services and permissions you want to give your users.
Once you've decided what you want in your sandbox, ARM templates will be a good choice for automating the creation process or a combination of scripts and templates depending on how much customization you want to be able to give your users.. Most services include example templates in their documentation as well as what is in the template reference. Another common way to create a template is to set up a resource group with all the services you want in an environment and export the template from the portal, though not all options are available in the portal export.