The CA will work with any controller with a throttle input. Both the throttle and the PAS plug into the CA instead of the controller, and for the PAS, it converts to signal to a throttle output. The CA requires battery voltage, and current as inputs, as well a speed input, and has a throttle output connected to the controller. It can get the speed and voltage from the controller. The version of CA that you’ll want has a shunt for sampling current, that’s placed in line with you battery conductor between the battery and controller. With those inputs, the CA can do a pretty large variety of things and provide a lot of data.
If you get one for your torque PAS, you will over time realize the other features and benefits. Some people say it’s dated, and while the screen is a basic non color LCD, there really isn’t anything, short of making something custom programmed with with Arduino, etc., that is available and performs similar functions. If you ever decide you want to upgrade your controller, you can just get a “dumb” controller and connect it to the CA and you retain all of your functions and preferences.
It’s sort of like the old days when audiophiles wanted component stereo systems, so they could change or upgrade components without replacing the entire audio system. For a lot of folks this is the preferred path, since good programmable controllers are pretty expensive to replace, and frequently costa lot more than a CA/dumb controller combo.
The one technical thing you need to be aware of is that torque sensing PAS units typically require around 10v to operate, so in most cases you will need a small buck converter to supply that, since most controllers or the CA don’t have that voltage available. You will need to deal with that regardless of how you decide to implement it, CA or no CA.
EDIT: Search the forum on Lishui controllers. As amberwolf pointed out, it's possible that your controller is a Lishui. You'll find a few threads on open source firmware for certain models of Lishui that support torque sensors. I didn't recognize your model number in the posts I saw, but that doesn't mean it doesn't exist.