The reason that there's no documentation that you need to do anything special for mountall to support /var on a separate partition is because you don't! You've pasted the appropriate lines from /lib/init/fstab for /var/run and /var/lock and as you can see, they both have the "showthrough" mount option
These causes mountall to take special action to mount /var, with these filesystems mounted on it and under it
This isn't true at all.
The reason that there's no documentation that you need to do anything special for mountall to support /var on a separate partition is because you don't! You've pasted the appropriate lines from /lib/init/fstab for /var/run and /var/lock and as you can see, they both have the "showthrough" mount option
These causes mountall to take special action to mount /var, with these filesystems mounted on it and under it