Yes, you can connect the controller directly to a computer via serial port. Using the response pad was just an idea to help you with the testing but it’s not required.
When set to E-Prime mode, the controller sends 800 or 1600 bytes per second, with each byte containing a bit pattern and each bit corresponding to a key. That’s how PST implemented it in their Serial Response Box (SRB) and the Lumina controller emulates that. When using the Lumina controller with E-Prime, you should be telling E-Prime that you have a PST SRB Model 200A.
It is possible to have the Lumina controller send ASCII characters – just set the mode to ASCII. But in this case, you will need to do some programming in E-Prime to open the serial port and read the incoming bytes.