From your description it sounds like you are getting a “combo” update from the App Store. This will happen if the current revision is more than one point release older than the update, i.e.
10.11.4 -> 10.11.6
10.11.3 -> 10.11.6
Etc.
You only ever get the “incremental” update if you’re going from one point release to the next, i.e.
10.11.5 -> 10.11.6
10.11.4 -> 10.11.5
Etc.
All combo updates contain all files that have been updated from the .0 initial release up to and including those for that update, i.e.
10.11.6 combo update contains all files that have been updated since the initial release of El Capitan 10.11.0
This means the combo update will include an updated boot.efi file. This will overwrite the Pike version. If this happens, when the machine reboots it will make the initial attempt to boot from your El Capitan drive but the boot loader will fail due to the Apple version of the boot.efi code expecting a 64-bit EFI ROM (original MacPros have a 32-bit EFI implementation in ROM). The boot ROM then discards the El Capitan partition from its list of bootable partitions and moves on to the next in the list, which will likely be your Lion partition which will have a 32-bit compatible EFI extension boot.efi.
You can fix it from your Lion partition. Simply copy the Pike boot.efi into the two documented locations whilst booted from lion. Choose your El Capitan as the startup disk and restart. Again I’ve written lots about this in this thread (as have others). Maybe search this thread for posts by me and contains cp boot.efi... post
#3614 is a good candidate
P.S. don’t forget that there are two utilities in this thread to catch the condition where an Apple update overwrites the Pike boot.efi file. Choose one or the other of capitanPikeFix or my Boot64 utility.
It’s worth pointing out for future reference in case you go for another build. However, once your classic MacPro reaches 10.11.6 the utilities become redundant (because there will be no further OS updates, therefore it’s unlikely that the boot.efi file will be overwritten)