Hi Erik,
Hopefully, someone who has this meter or has the better understanding of its schematic will chime in. My reply may not be particularly helpful.
ICL 8069, if it is present in the meter is the voltage reference IC. It is not used for low battery warning. As per schematic in reply #7, it is ZD1 and its output to ICL7106 is marked as R.
The following are my guesses which may be completely wrong.
The *whole display is not directly driven by ICL7106 but in conjunction with RA1-RA4, which is the METEX IC with a clock crystal on a daughter board in the picture in reply #11.
I guess the IC4 in the schematic is generating the low battery signal but I am not sure. My guess is based on the assumption that this IC is feeding signal to the display chip (RA1-RA4).
Edit: * correction. Also, I am not adding further explanation here in order to bump it and in the hope that someone might give better idea to solve your problem with this meter.