OS3R,
Are you using the Z-Controller to adjust track power, or just the Z1K brick connected directly to the track?
Even if it is in "proper" spec, the Z1K brick puts over 20 VAC on the track. The Z-conroller will drop the maximum voltage down by about 1.2 volts.
On the theory side, on the several LionChief and LC+ engines I've taken apart, there is nothing in them that should be damaged by voltages even up to 24VAC, however the designs have varied quite a bit from one engine to another, so it's probably a good idea to follow the instructions if they offer any recommendations on operating voltage for a particular engine.
That said, it is important to note that with modern transformers that use electronic voltage controls (Aka "chopped wave" or "shark fin wave" transformers) even f you set the voltage lower, the electronics in a LionChief/+ engine will see the maximum voltage that the transformer can provide. So, if you have a transformer of this type, and it is capable of supplying a higher voltage than what the LC/+ engine calls for, you shouldn't use that transformer.
In this video the gray meter shows the AC RMS voltage coming out of the Z1000/Z-Controller. The red meter shows the DC voltage that a LionChief/+ engine's electronics see at the same level. You can note that even with the throttle set as low as 8 VAC RMS the engine is already seeing the same internal voltage that it does with the throttle turned up all the way.
JGL