In Lively, web pages are worlds. Worlds contain live objects and can be saved in their current state. You can save a world to continue working at some point or to share a specific state. Just send out the link to the world ;-)
You can either save a world by overwriting or under a new name.
Right-click into the background to see the world's menu. There you'll find save world and save world as.... When you save the world under a new name, you get prompted for a name.
A faster way to save changes to the current world is by using the cmd/ctrl-s shortcut.
This world is nearly empty. You can use it as template for further worlds. Maybe you want to browse the PartsBin to find some interesting objects to explore?