Any type of battery, including lithium, of the correct voltage will work and it need not be quite as large capacity as 12 Ah. Although each battery inside the case is a 12 volt one, they will be wired in series to give a higher voltage. If there are two batteries in the case, it's 24 volts, if it's three batteries, it's 36 volts.
If you measure the internal dimensions of the casing on your bike (bike shown below), you may be able to get a pack that fits within it from a supplier such as Li Ping. However, it's more likely you'd need to mount an alternative battery on the rack and arrange connections for it.