I wouldn't try to flip the direction switch while the motor is moving. I regularly use the cruise control on my car, but I still come to a complete stop before putting the transmission into reverse.
Whether the controller has digital or analog inputs, you still need to generate the motion profiles somehow. This could be done by a human twisting knobs and flipping switches, but if you want automation then, well, it will require more. But, automation is a rabbit hole with no end. Digital inputs allow precise positioning. That means that if each part is chucked into the lathe at exactly the same spot, then you could program the tailstock to go to a specified position and stop. That sounds dangerous to me, but some controllers can be told to run the motor at a specified torque. That means you could program the motor to advance until the tailstock is tight and then stop. This is basically what you do when you turn the knob by hand.
I once help some students with a project where an automated vice would close to a programmable point by monitoring the current of a DC motor. It ended up working, but it was trickier than you might guess at first. Like I said, automation is a rabbit hole.