While SLA batteries are resistant to abuse and can supply very high currents, they have about half the energy density of lithium chemistries, in other words they're bulky and heavy for the power they produce.
The SE/30 monitor operates from 12VDC which is produced by the power supply. 120VAC goes into the power supply, is rectified and filtered to 160VDC, chopped and fed to the high frequency transformer which steps it down to the required voltages. These are rectified and filtered to produce the 12V, 5V and -5V rails. If you wanted to run it from batteries, it would make the most sense to start out with something like 16VDC from a set of 4 Li cells in series, then use DC-DC boards which can be had for <$5 each to step it down to the various outputs you need. Some creativity would be required to allow the internal PSU to seamlessly power the machine but it could be isolated from the batteries with a Shottkey diode on each rail, or replaced entirely with a charger having enough grunt to power the machine while charging.
The SE/30 monitor operates from 12VDC which is produced by the power supply. 120VAC goes into the power supply, is rectified and filtered to 160VDC, chopped and fed to the high frequency transformer which steps it down to the required voltages. These are rectified and filtered to produce the 12V, 5V and -5V rails. If you wanted to run it from batteries, it would make the most sense to start out with something like 16VDC from a set of 4 Li cells in series, then use DC-DC boards which can be had for <$5 each to step it down to the various outputs you need. Some creativity would be required to allow the internal PSU to seamlessly power the machine but it could be isolated from the batteries with a Shottkey diode on each rail, or replaced entirely with a charger having enough grunt to power the machine while charging.