The circuit you have attached will trip below a certain point and untrip that same certain point. It sounds like you need a gap between the trip and untrip point. In which case you need a window comparator. Have a look at this circuit: https://cds.linear.com/docs/Datasheet/1042fa.pdf
You should learn about Lithium Battery Charging at www.batteryuniversity.com .
When the voltage drops to 3.7V then there is plenty of charge remaining. Maybe 3.2V or 3.3V would be low.
Also when the charging battery voltage reaches 4.2V then the battery is only 60% to 70% charged. The charger should continue charging at 4.2V until the current drops to about 2% of the battery capacity which takes time but will fully charge the battery.
You should learn about Lithium Battery Charging at www.batteryuniversity.com .
When the voltage drops to 3.7V then there is plenty of charge remaining. Maybe 3.2V or 3.3V would be low.
Also when the charging battery voltage reaches 4.2V then the battery is only 60% to 70% charged. The charger should continue charging at 4.2V until the current drops to about 2% of the battery capacity which takes time but will fully charge the battery.
But when the charging voltage reaches 4.20V then the cell is only 60% to 70% fully charged. Extra time must be spent at 4.20V until the charging current drops to 3% of the cell's capacity then it will be fully charged.
2.75V is too low for a modern (cobalt type) rechargeable Lithium cell. Then the cell might ignite when it is attempted to be charged. Most Lithium cell chargers will (should) refuse to charge a cell with a voltage below 3.0V.