Multimeter precision on low battery
It depends on the detail of the meter. A cheap one is likely to be worse than a name brand one. If you can borrow another meter, I suggest you calibrate the suspect one against it, with varying battery voltage.

I did this with my meters, and was horrified.

I measured a fixed voltage, while powering the meter from a variable supply. I reduced the supply voltage, while monitoring the measured reading, and the state of the LO-BAT indicator.

Only one of my meters popped the LO-BAT before its reading deviated by 1%, and it was a cheap one.

All meters took 9v batteries. One meter quit before it got down to 7v supply. One meter kept going to less than 4v, and that was a different cheap one.

There's no need for guesswork about your meters. Measure them. Put a red sticker on any that can lie to you about their accuracy.