Yeah, this is definitely a 3-phase machine.
Wiring a second motor driver in parallel with your Y-axis driver will be the easiest way forward for you.
You will need to buy a biphase stepper driver (Cohesion3D sells a decent one and it’s guaranteed to work, otherwise look for a Leadshine elsewhere - should run less than $40 to your door).
You will need to add jumper wires from the existing driver’s control signals to the new driver’s control signals. You will also need to add jumpers from the V+/V- terminals to the new driver’s V+/V-. In this setup, you have two motor drivers running from the same controller. It would be worthwhile to add a second connector of some sort to connect the rotary stepper motor as-needed.
When you want to drive the rotary, you will disconnect the Y-axis round connector as pictured above, and plug in the rotary to the new connector. After positioning the y-axis gantry at the right position everything should work as necessary.
Also note that Ray doesn’t write Lightburn - there’s a separate forum to discuss that on the Lightburn website, and the lead developer is very responsive and helpful. In fact, he monitors this forum as well and may be able to help or direct you to the right place.