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A low voltage disconnect is used to stop loads from dragging a battery bank below a given voltage.
In most installations all loads go through the LVD except the inverter, due to the heavy current draw. The inverter will have its own internal LVD.
Lead-acid deep cycle batteries last the longest with best capacity if they are never cycled more than 50% Depth of Discharge1). That point is somewhere around 12.10v.
LiFePO4 nominal 12v banks can be safely drained to 80-90% Depth of Discharge. That point is something like 12.0v.2)