First part was to disassemble the keyboard and follow all the traces of the keyboard matrix so I knew where each key was connected.
Then I had to unsolder the keyboard's ribbon cable connector from the typewriter main board. during this step I broke a pin of the connector which I replaced with an LED pin I had lying around...
A Teensy (3.2) was used for this project since it's easy to build a USB keyboard with it. (A lot of custom mechanical keyboards use them) I Soldered the connector to it in a way that I could solder the most pins directly unto it. The rest of the pins were connected using some wires.
Unfortunately I realized later that I soldered the LED's Ground pin to a digital pin of the Teensy, at this point I was too lazy to unsolder the connector so I left it like this.
Programming the Teensy 3.2 turned out to be pretty easy since it has a lot of feature out of the box for making an HID Keyboard. I decided to write the code myself to learn more about how keyboards work but there is a lot of already made keyboard firmware available for the Teensy.
The code is on github: https://github.com/pboardman/DLX400HIDKB
The last step after debugging the code was to put the keyboard back into it's case and test it out!