Not sure what booster you are talking about to charge the lithium battery. You posted a question about a charger that plugs into AC.
There are SCCs available that can also charge from an alternator.
Edit: What specific model booster? I think this is a 40 amp DC to DC charger, but with using it with an alternator, I don't know if it would automatically shut off if the motor were off to prevent the vehicle battery from depleting. Also, during certain times like idle, I'm not sure there's excess production in the alternator to charge. The owners manual should say. Renogy does a pretty good job at docuentation.