You really do not want BMS to disconnect battery as the primary low voltage detection. There are several potential issues doing this, relating to surge currents on restart. If you have a battery monitor for AH tracking you may also lose the cumulative AH info.
If you have an adjustable inverter low battery cuttoff, and you are unable to get an acceptable low battery inverter shutdown, it is usually caused by too much battery cable voltage drop on peak current demand (too small battery line wire gauge) or insuffcient battery size to support peak current demand.
With LFP batteries with a low cost BMS, the BMS MOSFET series switch resistance also comes into play during peak surge current voltage slump. Their switch resistance relates to their max current rating. Many of the low cost BMS current ratings are based on their peak current capability before they self destruct and should not be used with a continuous current greater than about half their specified current rating. They have an overtemp shutdown but that does nothing for surge current voltage drop across the BMS.
If inverter has a low battery voltage trip delay timer adjustment setting, it can be used to ignore momentary peak current DC input voltage slump.
If you allow batteries to get significantly out of balance it can impact on how low battery detect reacts. You will get significantly less capacity for battery array so original battery monitor AH capacity setting will likely be far off. When cells get to less then 20% state of charge their voltage slump under heavy load current will be greater, particularly if current peak last longer then 20-30 seconds.