Rated IR is usually under ideal conditions with auto shutter, etc. Most folks in reality see half of what the IR says.
Since we are using it for LPR, it is an unique use case and is bouncing off of reflective plates, so the LUX rating isn't as critical (within reason).
Which budget PTZ are you looking at? Again, let the users here that have experience with specific cameras let you know...for example I know a Sunba will not work for this (I have one and have tried it at night and will not work)...or a JideTech as people have tried those and didn't work...The budget PTZs will not let you set a shutter speed or ignores it to give you a bright image...
As I mentioned, most PTZ cameras by the way are not suitable either for LPR because you cannot manually set a focus, so even if you can truly set a shutter speed, it cannot force a focus and the focus always changes based on what the image sees and with the image black at night, it may be useless.
Some people have had success by not using it as a PTZ and forcing it to B/W 24/7, but it is iffy on success. Some of the Dahua and Amcrest PTZs have the ability to semi-auto or manual the focus, but that has to be done right then and there - if you move the PTZ and then move back, it will not be in focus. But at that point, you are above the cost of the Z12....
Remember, at night, the image will be completely black except for the head/tail lights and the plate, so most PTZs at that fast shutter will not have anything to focus on and then when a car goes by, it will be blurry...
If you cannot truly set shutter and focus and the other parameters, then it doesn't matter what the LUX specs say...but if it lets you set shutter but then the software automatically ups the gain to 100% and you cannot change it, it will be useless as well...that is the problem with many budget cameras is the inability to force settings as they have wrote the firmware to adjust other parameters in an attempt to give a bright image, but then motion goes to crap. The inability to be able to truly set parameters will fail for LPR...
You can go down this rabbit hole and maybe get lucky, but why not use the experience of folks here?
But really, if you mention the PTZ you are looking at, someone here may have one and be willing to give it a try at night and see if it can work to see plates....