Yes, it's possible to use a Lithium battery with your Axpert 3kVA 24V inverter system, provided that the inverter is capable of charging Lithium batteries safely. You may want to check the manual or contact the manufacturer to confirm this.
As for recommendations for the Lithium battery, you may want to consider using a Lithium Iron Phosphate (LiFePO4) battery, as these are known for their safety, durability, and long cycle life. The size of the battery you'll need would depend on your specific power requirements and usage pattern, so it's best to consult a specialist for a more accurate recommendation.
In South Africa, there are several suppliers of Lithium batteries, including Battery and Solar Solutions, AGM Batteries, and Energon. You may also want to check online for reviews and compare prices to find the best option for your needs.