Is this a company computer? If it's a personal computer, LV 2020 Community Edition is coming out next year. It will be LV 2020 Professional for free - provided you use it for personal use only.
For what it's worth, I have LV 8.2.1 installed on my Windows 10 machine and it seems to work OK. I don't do any development on it, but it runs and opens ancient files for conversion to 2016+.
I have older versions than 7.1 back to 5.0 running under Windows 10. Of course not for any real development work but for archeological research 😀.
7.1 (and to some lesser degree 7.0) was the first LabVIEW version that you couldn't just copy the installation folder from a different computer to get it working as its installer wanted to do all kinds of registry and system related changes that will make LabVIEW puke on startup if they aren't properly setup. All earlier versions I got on this machine simply by copying them from an old installation image. As far as I remember the 7.1.1 installation went smooth on this machine but that was 3 years ago with a Windows 10 version that was substantially different to the latest and greatest from this fall. With the old Windows versioning scheme the current version would likely be called Windows 2019 or something and be considered a very different installation than the original Windows 10 at the time of its release.
With the current state of technology the only feasible way of installing such old software is indeed almost always through Virtual Machines. The holy cow of backwards compatibility has been abandoned by most companies nowadays as its cost gets prohibitive with basically an exponential curve as time goes on. Also with Microsoft, who was at one time one of the strongest defenders of it.