That's pretty much it.
Also would any chassis ground count as being "common" so long as the Van's battery and the house lithium batteries all have negative continuity to it?
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That's pretty much it.
Also would any chassis ground count as being "common" so long as the Van's battery and the house lithium batteries all have negative continuity to it?
You will want to match voltages: starter electrical system to DC-DC input; house electrical system to DC-DC output. You will also want to insure you don't overload the starter/alternator electrical system when charging the house battery and/or supplying house loads.
Generally, you'll want to set set up the DC-DC charger so it only charges the house battery when the alternator is running. Otherwise, you could drain the starter battery.
As far as starter battery type, no I don't think it matters.
I don't recommend using the chassis as an electrical return path for your house system. Run separate negative leads from each load and charging source back to a common point. Then connect that common point to the chassis. That way, no house current flows through the chassis and you keep the house electrical system clean and free from any chassis currents from your vehicle electrical system.
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