Serial Monitoring of DB25 Parallel Port Data
Just parallel plug it into the Arduino. Tap it like the old serial break out box days. Either make yourself a Y cable to repeat the pins to another 9 pin connector, or buy one of these:-



Then you just read the 8 data pins with a Arduino as a port read instruction (say PINC). You may have to play with the wire order to get sensible codes. Then send the byte over the Arduino's USB cable (using Serial.print(byteValue) ) to the PC running terminal emulation software like SCREEN or PuTTY.  Try to run the printer at a low speed, say 10 kBaud.  The Arduino software is surprisingly simple.  I estimate 10 - 15 lines plus a quick interrupt service routine.

You'll find that in order to discriminate one byte from another passing along the cable, you'll also have to access the /STROBE line on pin 1.  If you connect this pin to the Arduino as an interrupt, you should be able to read the 8 data bits on every strobe signal.

The old Centronics ports ran fairly slowly so the additional impedance of the Arduino's input ports and Y cable shouldn't load the industrial equipment's printer port. The interface was 5V so get a 5V Arduino to avoid level issues or catastrophic explosion of a 3V one.

Essentially you'd build a logic analyser, which you could also just use if there's one lying around.  Mixed signal oscilloscopes are good for this too.