It seems the feature to display calendar events on lockscreen has at least become obsolete since lollipop:
With Android Kitkat and earlier, you could install apps that would display your calendar or other info on the lockscreen. With Lollipop or later, Android removed that feature.
However with a plethora of 3rd party lockscreen apps it is possible to get this working.
For such functionality please refer to this list of potential lockscreen candidates that allow one to view upcoming calendar events.
From that list and ones suggested in comments, I personally find these useful:
Hi Locker's offers a CyanogenMod-style quick launcher that works by holding and swiping over to one of your favorite apps to quickly open it from the lock screen. It has 3 styles of lock screen: classic, Lollipop and iOS, and a separate screen dedicated to your calendar, where you can quickly view upcoming events.
Next Lock Screen looks elegant and simple, but beneath the surface it's cleverly calculating which apps you're most likely to use based on your location (home, work and so on), then presenting you said apps. You don't need to use this feature of course, but Next is still worth using for its neat presentation of notifications, calendars and other key phone functions.