A LiFePo4 battery charges just fine with the OEM alternator, it just can't charge the battery to 100%, but only 70-80%. The alternator has nothing to do with the discharging of a battery in general. The lithium batteries have built in battery management units (BMUs) in order to protect them against overcharging, overcurrent, charging at too low temperatures, overheating as well as undervoltage. They can cut off completely while driving, which is critical in older cars. That's why a car needs to be designed for a lithium battery or there are specially designed lithium starter batteries, which makes them very expensive.