Hi,
a time ago i got the recommandation for inplace upgrade if Zimbra is running on Ubuntu from the official Zimbra Support.
The recommendation was:
° upgrade Zimbra to a version supported on both Ubuntu LTS Version
° stop Zimbra and remove startupskript
° do-release-upgrade
° reinstall same zimbra version for current Ubuntu
For the migration with 8.7.11 from Ubuntu 14.04 to Ubuntu 16.04 there was special special step reactivating there sources.list during do-release-upgrade.
But i have done this already several times in the past.
greets
Thomas