I run a domestic 240-Volt audio-visual system off-grid in my motorhome, from 12 Volt battery power.
Two 100 Amp-hour lithium batteries are recharged from solar, the alternator or mains, if connected. I use a 2000-Watt pure sinewave inverter and power a Marantz AV receiver, Sony universal disc transport and KEF powered subwoofer.
Some basic physics implies that very heavy currents are drawn when the inverter is running close to full power. A couple of hundred amps is normal.
All lithium batteries must include internal overload protection, and often these circuits have very limited current capacity. In this application, the most important specification is the maximum current that can be supplied by each battery through its protection circuitry.
The energy stored in each battery is quite small, about 1 kilo-Watt Hour - enough to run a hair drier for half an hour.
There is some irony that a very pure power supply has to be converted to AC and then back to DC in each audio component.