One of the considerations is that the Lithium has good BMS (Battery Management System) built in. Lithium's have a sweet spot (high - low voltage) for operation, the BMS controls this. In the case of the one you show, it does. Lithium's require higher voltage and current to charge than lead acid types (Lead = 13.7V max, Lion = 14.7V max). Many converters can accommodate this up to a point, but as the previous post mentioned, if not specifically designed for it, your converter may charge a little slower. Worse case, your Lion will not fully charge and you will need to get a new converter to get full capability. Maybe consider an upgrade to an inverter/charger while you are at it. My 2-cents.
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