Yes you need to address this.
He thinks he's very clever, doesn't he!
I would make sure to respond to every email like this copying someone else in.
'Dear X,
Blah blah arrangements fine etc. I was however very concerned to read your latest attempt to smear my character by making reference to an 'event' which did not happen (your obtuse reference to some 'stairs incident').
As a result, I'm copying X into this reply, with their permission. I'll be doing this with all emails from now on, so you can be assured that there is a witness to your statements (Perhaps it will also help you 'feel safer'!)
Let me be very clear - I have no intention of allowing you to get away with making completely fabricated accusations against me. Although you are deliberately unclear in your reference to an 'incident', it's obvious that you intend to make an indirect accusation of some sort of abusive or inappropriate behaviour on my part. I have no idea what your intentions are in doing this, but as it's not the first time this has happened, it's clear to me that I need to create a paper trail of this behaviour, and independent witnesses, for my own safety. Let me also tell you that I am fully aware of other accusations you've made against me, and rumours you have tried to spread, via other people. I am also aware that such malicious behaviour may spread to you trying to affect my work environment. Let me be utterly clear - I fully intend to create a paper trail for this purpose too and I will not hesitate to involve the authorities if your malicious communications continue.
Let me be clear again. There was no 'incident on the stairs.' Let me say now in this now-witnessed email that I am utterly concerned that either a. you are for some reason starting a campaign of malicious communication or b. you may have some undiagnosed mental health issue. You may be interested to know that more than one of the people you have tried to turn against me with other bizarre claims are also concerned that the latter may be the problem.
Our relationship is over and it was entirely your doing. I suggest you move on more positively with your life rather than trying to attack me to make yourself feel better.
I will also not be meeting you again without a witness.
Regards,
Worried.