When the lithium batteries are in a vehicle being towed I think an isolated DC DC Charger is more appropriate. It is such a long run from the start battery to the lithium battery that there will be quite a bit of voltage drop. You wont really be able to say that the two batteries are sharing the same negative as a result. The charger should go next to the lithium battery so there is minimal voltage drop between them. Then the charger will be able to compensate for any voltage drop on the long route from the start battery.