I think the answer to this would depend on what’s causing the lag. If it’s because of some app that’s creating a delay, and you put that same app on the new phone, then you’d very likely see the lag on the new phone.
If the app is because the Moto X4 is struggling because the processor is maxed out, then again, you could see the same problem if you load the Z4 up with the same apps. If it’s because the X4 is out of memory and struggling to render the screen then a new phone is going to feel zippier… for a while.
I think this is why @jben was trying to dig into what might be causing the lag on the X4.
Comparing the tech specs, the Z4 does have more RAM (4GB vs 3GB on the X4) and internal memory (four times as much), but it actually has a slightly slower processor, though probably not different enough to really notice.
The graphics processor probably plays a role in screen rotation, and the Z4 does have a graphics processor that’s a step up from that of the X4, with better benchmarks in reviews I was able to find online.
With the Moto Z4, you’re still looking at a phone that’s already 2 years old and may be nearing the end of its battery life. Is there a reason you’re particulary interested in the Z4?
If you do go with the Z4, please be sure to let us know what you think. The Community Treasure Chest has some accessories for the Z4 that I’d be glad to send you a case and/or JBL Soundboost Speaker Moto Mod if you decide to get that phone.