The question as phrased does not compute. The idea that my batteries could drop to a SOC that was so low it triggered the alarm without me being fully aware it was going to happen is just foreign to me. Kind of like being "surprised" by a low fuel
light coming on when motoring down the highway. I am pretty tuned in to our batteries, at any point in time--without looking at the gauges--I could probably tell you the SOC within 5%.
But... more in the spirit of the OP's question: When my batteries get down to the lowest "normal" state of charge, the generator
starts automatically, and runs until the charge acceptance drops to the point where I know they are about 93% charged. This is not a lithium
bank, but my logic would be very similar if they were (although the settings might well be different).
All this is controlled by a Victron Cerbo. The generator
is a WhisperPower 3.5kW DC genset that runs through its autostart cycle when the Cerbo closes a relay, and continues to run until that relay opens.
Here is the logic: From 0600 to 1800 the generator comes on if the SOC drops below 65%. In our world this effectively means the generator starts every other day at 0600. Outside those hours, the generator will start if the SOC drops below 55%, I can not remember the last time this happened.
The generator runs until the charge acceptance drops to a level I have found equates with 93% SOC. I use charge acceptance rate, because it is a very accurate indication of SOC for these AGM
style batteries. From 93%, a normal solar
day takes me to 100% by the end of the day.
This system has worked well for us for almost 3 years. When these batteries die, eventually, I'll probably go with Li, but that is a long way away, and its way too early to predict what will be state of the art at that point.