No standalone version of the calendar app is available. And if you're just interested in Lightning Calendar and not Thunderbird, the app will have additional functionality and interface elements that will get in the way of using the calendar.
Being that this is a Google app it is proprietary which means Google hold full control of the app. Though there are APIs there is no official app on offer other than a Chrome Webstore app and the webpage. This can limit how one uses the official interface of the app.
Yorba, the group that developed California, is no longer actively developing software. While Geary (Yorba's mail client) has been adopted by the elementary teams as "Pantheon Mail", both elementary and Gnome have their own calendar projects and it is unlikely that either of them will