Today View on home screen

I think I may have figured it out. It may be that your Calendar app accidentally got locked into a different time zone. Try this:

Open Settings | Calendar and make sure that "Time Zone Override" is either turned off or is set to your home time zone. If my hunch is correct, you have accidentally turned "Time Zone Override" on and set "Time Zone" to a time zone other than the one you call home. Good luck.

Is your Calendar app set to display events in a fixed time zone, regardless of where you are visiting?

If, for example, you live in Roma but travel a lot to London, you might find it sensible to fix your Calendar app's time zone to Central European Time. When you are in London, the Calendar widget doesn't know this, so it will display the event in British Standard Time, one hour earlier. If you enter a lunch date for 12 noon without adjusting for the time difference, your widget will display the event as 11AM, since that is the time you should be caring about at the moment.

Is this what is happening to you?

When the times diverge, which information is "correct" and which is "incorrect"? Is the Time of Day on your Lock Screen correct? Are appointments shown on your Today View correct or incorrect? Are appointments shown in Calendar correct or incorrect?

So, in what manner are they different? Are the differences between the two tools entirely consistent?