Show limited reminders/notifications on iPhone lock screen (iOS 13)? I'd like to be able to show on my iPhone lock screen notifications that I have upcoming events today, timed reminders, and suchlike, but without showing the actual details of what they are. However, I can't work out how to do this.

The "Today View" screen (swipe from the left) doesn't seem to respect the Notifications "Show Previews" setting (ie, "When Unlocked") and shows the calendar event or reminder titles regardless (rather than just (eg, "Event at 15:00"), which is definitely not desirable from a privacy perspective (eg, if your phone is stolen or lost, someone else would be able to see this information, which should be private).

The Notification Centre doesn't seem to be very much help: although it does only show limited information when my iPhone is locked (good), it seems to entirely forget about upcoming events apart from when the set notification time arrives. I'd like to have that reminder of upcoming events or reminders constantly available (albeit with details only visible when unlocked), so that I don't forget about them (that's why my phone is supposed to be remembering these things for me!).

(I've also just spotted that although I have Badges enabled for Calendar, the Calendar icon doesn't seem to show them, which would also be a useful memory jog, if it was working?!)

Is there some way that I can adjust the settings to do what I want?
Settings > Reminders > Disable banners, but leave sounds on. 
Your iPhone will make a sound and vibrate when you the set time or date comes, but nothing will slide from the top screen. From there, you can prevent the notifications from appearing in Notification Center. If you want to see the reminder, you'll have to open the Reminders app.