Is this a Google linked calendar? What you describe sounds very like what Google do with invites.

Nothing to do with Google, no, but it's a good thought whether something else could be doing it behind the scenes. The thing that makes me think it is Thunderbird is that a message shows saying something like "This relates to an event that has already been added to your calendar."

What email provider are you using? I know Google do it. But the other free providers have an option as well.

It's a work Exchange account. I will check this out, but I don't think it's the case because as far as I remember it didn't happen before I was using Thunderbird/Lightning.