The G540 is intended to be controlled by a PC's IEE 1284 host parallel port.
See
https://web.archive.org/web/20040616170240/http://www.fapo.com:80/1284elec.htmfor electrical specs.
You must *ALWAYS* connect Gnd. For short jumpers you can probably get away with a single Gnd wire, but if you are using a longer cable all Gnds should be connected for good signal integrity.
Although outputs using 3.3V logic levels *may* be compatible with a IEE 1284 device port's input lines, it isn't certain if your SoC board can supply enough current - a non-isolated logic input wont load it heavily, but if the interface is actually optoisolated, significant drive current may be required - the standard calls for +/-14mA, but the original IBM implementation (pre-standardisation) Data Out pins were originally driven by a 74LS374 octal latch, which could source 2.6 mA and sink 24 mA.
You may need to measure the current one G540 input draws, using a 3.3V supply with a 50R series resistor. Also, check that any output lines don't exceed +3.3V when high, before connecting them to a SoC input.
If the electrical specs aren't compatible, or if you want to use a long DB 25 cable, you'll need to use level translating line drivers.