Typically, inverters do not mind running on lithium batteries. As long as they are in the right voltage range (12, 24, or 48 volts), they should work. However, you should change the low voltage cutout, if the inverter has one. Lithium battery manufacturers will provide a recommended low voltage cutout for inverters.
In general the best inverter for lithium batteries is one that is fully programmable. Our preference is the Victron line of inverters because they can be programmed for very specific voltage and charge profiles.