Same deal. iPhone 6 Plus. Original LCD, never been repaired, been protected and treated really well, yada yada.
Started having issues about three IOS 11 upgrades ago, so probably 11.0.x or 11.1. Didn't pay attention until I realised that something was seriously wrong and I'd been through an upgrade or two and the problem was still there.
The touch screen locks up randomly.
The touchscreen fires random keystrokes - just hovering a finger above the screen will fire a stream of garbage into a text message for example. Trying to touch a specific key on the keyboard will fire the wrong key or keys - before the finger gets to the keyboard the touchscreen has already chosen a different key.
In horror I watched the touchscreen scroll through my messages in Outlook - one every second or so, working its way down my inbox, marking each as read. For me read/unread is a primary marker of whether a client issue has been handled. By the time I noticed, and realised, what was happening, grabbed my phone from my desk, and closed outlook, I had about 1/2 day of detective work to do to get my erstwhile 'to-do' list back together.
Notice that the phone was laying flat on my desk - my hands nowhere near it - but unlocked with Outlook open (which is unusual for me - security is a concern) - and the touchscreen was still going haywire.
I spent, literally, 45 minutes trying to send a three sentence SMS. Required a lot of lock/unlock cycles (usually unfreezes the touchscreen). Then with the touchscreen firing a stream of garbage into the keyboard, and the keyboard auto-correcting that stream of garbage even as I tried to delete it, and then the touchscreen wholesale freezing every other millisecond, it just became impossible to get those three sentences in place and sent. Oh, and it was screwing with the recipient list even as I was trying to edit the message body. Incredible stuff.
Then there's the routine inability to even unlock the phone. Touchscreen freezes. Can't unlock iPhone. iPhone is a brick in a shiny case. Business day stops until iPhone wants to work again. Power off/Power on. Wait. Hope.