Could be a few things tbh.

First stop would be to check for air leaks, being an air dependent system if there is even a small leak anywhere the flap wont move down enough to meter the fuel into the cylinders, more noticeable when the engine is cold (take off the air filter and check to see the flap bobs up and down reasonably whilst you crank)

It could also be the car is running lean and not providing enough fuel for cold starts as a result of how its set.

It would also be worth checking the CTS as it is quite a key component in the cold start process.

How does the car drive onc its up temperature? The K jetronic system is fail safe and will still run even when something major on the fuelling system fails, but they are a slag to start cold and run ok-ish once up to temperature.