To get it partially working in both:
Subscribe to a new "Calendar" - choose ICS and subscribe to:
http(s)://mail.example.com/home/<user>/Tasks
Now, you can create tasks on the task pane, as long as they are associated with Tasks. They'll show up online as well. You can mark them as completed. If you choose "Hide completed tasks", they'll even disappear.
To add a task, you should right-click in the tasks pane and choose new task, then you can select the Tasks calendar from there.
What's still broken:
- No way to delete them within TB. (Old ICS bug.)
- Quick add is almost useless, since you can't be sure which "calendar" it is adding to. (Work around, make sure the "Tasks" calendar is always selected.)
Overall, it's still frustrating how poorly Lightning and Zimbra work together. Tags, categories, etc, never copy across (for me). At least 0.8 is starting to work better!