What brand/type lithium batteries do you have? You mention 3 sets of 4 cells and two battery
packs with a lead acid battery
to protect the alternator
. This sounds like you have 4 cells in series and 3 sets of these in parallel x 2 separate battery banks ..... do you have a cell balancer across all 12 cells in each battery bank so all the cells in that bank bank are at the same voltage?
If you have all 12 cells balancing together for each lithium battery, then a trickle charge at 13.2v will keep all the batteries from discharging to the point of failure or damage, the lead acid battery at a high enough voltage to avoid sulphation and all the lithium cells at 3.3v, roughly half way between 100% SOC and 0% SOC and they will be happy at that for ages ..... but if you do not have all the cells balancing together so they each hold the same voltage, then follow Franziska's advice
and disconnect everything from the lithium batteries, including being linked to each other across the whole system. One cell going low in any of the 4 cell series strings will kill all the other parallel strings connected to it. All BMS systems require some electrical
power to run, if you have no charging connected to the batteries, the BMS will drain them flat and they will gradually destroy each other.
If you leve them om a trickle charge, no matter how low the voltage, and do not have all the cells balancing together, at least one cell from each group of 4 cells in series will gradually climb higher the the voltage of the other 3 cells .... resulting in at least one cell in each group with its voltage gradually dropping, yet the voltage across the battery remains the same ... until one cell dies, then it will kill the other batteries in parallel because they will constantly try to send current
to the battery with the weak cell .....
This is he major problem with linking 12v lithium batteries in parallel, all the cells in that battery group must be balanced to each other all the time to stop cell voltage run away ....