As documented here and elsewhere, the windows subsystem for Linux is currently in beta and therefore not available on Windows 10 Long-term Service Branch. My experience on LTSB is that you could enable the WSL feature but Windows Store wouldn't download the distro appx.
A few days ago I noticed an MS howto beginning:
"There are several scenarios in which you may not be able (or want) to, install WSL Linux distros via the Windows Store. Specifically, you may be running a Windows Server or Long-Term Servicing (LTSB/LTSC) desktop OS SKU that doesn't support Windows Store, or your corporate network policies and/or admins to not permit Windows Store usage in your environment.
In these cases, while WSL itself is available, how do you download and install Linux distros in WSL if you can't access the store?"
This led me to think WSL would be available on LTSB. However, I find the same "unsupported version" error when I try to install the package. Also the MS howto doc looks a little rushed (bad links, grammar/spelling errors) so I don't know how much stock to put in it.