Had a moment and I decided to try designing something similar.
This is what I got. It has self-latching, so once it triggers, only removing the power will reset it.
Will probably need some tuning when doing the real thing.
C1 will will ensure that Q3 doesn't receive any power at power-on, so Q2 forcefully turns on before Q3.
Also will filter the noise when connecting the battery and prevent too easy triggering.
D1 will quickly discharge C1 when power is removed.
At first, Q2 will be always turned on, until the input voltage gets low enough to release R2.
R2 will slowly charge C1, until it turns Q3 on. At the same time, Q3 emitter will turn on Q1, permanently latching Q2 base to gnd, no matter the Vinput.
I omitted any zener or regulation circuit.
Since a bipolar transistor base-emitter union has a 0.6V threshold (Yeah, not amazingly accurate, but I think it's okay in this application), a simple voltage divider might work.
Adjusting RV2 should be enough to correct any transistor tolerances.
In simulation, the circuit cutoff range was between 4.2V(RV2 set to min.) and 2.9V (RV2 set to max), the complete voltage range of Lithium batteries
I'm not a designer engineer so don't blame me too much!