So... an update...
Went back to ATS, they confirmed no new TPMS sensor had been damaged/replaced during the tyre changes, but checked with an Autel MaxiTPMS tool and confirmed that one of them was not giving any reading.
Contacted my local Lexus dealer (as I'm booked in for a 100k service next week anyway) and they said they'd be happy to take a free look as I'm coming in next week anyway.
On the way to the Lexus dealer, the TPMS light suddenly went off - checked with Carista on arrival and that sensor was no longer giving an error, all 4 were reading.
Lexus took a look anyway and confirmed all 4 batteries were still fine. They said after a tyre change, sometimes the sensors take a while to "re-activate", adjusting to a large deflation/re-inflation which throws them off. It took around 150 miles of driving to re-activate it, but all is working fine now!