Yes, a 14-volt inverter can use a 12V lithium battery. Generally, 12V inverters can handle automotive voltages that may exceed 14 volts, so your inverter should be fine with a 12V lithium battery1. Additionally, a 4S LiFePO4 battery pack, which is a type of lithium battery, has a fully charged voltage of around 14.4-14.6V, making it compatible with a 14V inverter2. [pdf]
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