I've only just found this post!
I'm having the exact same issue when charging, screen becomes unresponsive and laggy.
For me so far, it seams to be only with the stock charger, and also much more noticeable the lower the amount of charge is in the battery. If the phone isn't charging rapidly it doesn't seem to happen (or when it does is much less annoying or noticeable). Using a 1A or 2A charger it seems to be just fine with. I don't have an 3A chargers to test (or any that seem to trigger the 'charging rapidly' notification, not even my Nexus 10 one) to test to see if it is just the supplied charger or a fault in the phone when charging rapidly.
I took mine back to Carphone Warehouse today and they wouldn't swap it as they believe it is only the cable at fault (possibly to do with the shielding in the cable) and therefore they don't replace it, they just replace the cable via LG (which they didn't have any spares to replace it with).
They didn't have any cables to test the fault either, nor any way to check the draw of the phone while charging using USB-C to USB-C. They used an ebay looking USB-A to C cable with a 2.1A charger. The phone drew the full 2.1A when the screen was off and the lock screen stated it was 'charging' (so not rapidly). The draw dropped to 0.5A when we started using the device. While using the device there was a vary vary minor slow down and lag, but not enough to affect typing on the keyboard which is my main issue when charing with the stock charger. The only visual sign of any slowdown was animations were laggy every now and then. This wasn't enough for them to believe it was a phone fault, so I still have the original device and without a cable replacement as they don't have any USB-C cables to do any further tests.
They basically told me to find another charger that I can bring in that also causes the fault and only then would they consider replacing the device and cable. Not the best customer service considering they were meant to be the 'Geek Squad' but didn't even have the equipment needed to test the device properly. I also only have till tomorrow, as thats when my 'return to store to replace' warranty runs out, after that it'll be a 'send off to LG' job.
Anyone seen anything from Google about this recently? I can't seem to find anything online about it other than a few posts on here.