Lag on 4k external monitor and MacBook Pro (early 2016, internal graphics) running in retina mode: can bad cable be a reason or just not enough power?
So, if I read your question, and understood it correctly, you are using a USB-C cable to connect your screen to your machine?
The thing is that a USB-C type cable is not the other!
There are a lot of differences in USB-C cables so you have to be sure that your cable supports what you want it to do.
If the cable's bandwidth is not sufficient for supporting 4K it can result in lags as you explain.