Hi Allie4140 (Eva).
Is the DC-DC charger one like this?
https://www.renogy.com/12v-dc-to-dc-on-board-battery-charger/
As is also shown in this video?
If it is, then you can connect the DC-DC charger the following way:
Starter battery - fuse - long wire - DC-DC charger - short wire - lithium battery.
(It is most likely recommended to place the DC-DC charger close to the lithium battery, as the DC-DC charger will eliminate any voltage drop in the power line/wire, going from the starter battery to the lithium battery. )
And then you add a small switch in the "D+ signal cable".
This switch carries hardly any amps, so it can be any little easy-to-place switch.
This way you can chose to use the DC-DC charger, ONLY when the switch in the "D+ signal cable" is on.
If you connect the other end of the "D+ signal cable", to a location in the wiring system of your car, that only has power when the engine is running, then you have the double security of the DC-DC charger only being active and ON, when both situations are true.
As in: when both; the motor is running, AND when the switch in the "D+ signal cable" is ON.
You can add a Main/Kill switch in the power lines, but it is not necessary, as there is already a remote-controlled Main/Kill switch built into the DC-DC charger.
And this remote Main/Kill switch is ONLY ON, when +12V is supplied to the "D+ signal cable - screw terminal" on the DC-DC charger unit.
So when the "D+ signal cable - screw terminal" on the DC-DC charger unit, is NOT connected to a 12V source, then the (built-in) remote-controlled Main/Kill switch is OFF. And no charging of the house/lithium battery is happening.
I hope this explanation makes sense ? Otherwise, please ask more. Okay?