I think you're right that Lightning (the Thunderbird calendar) doesn't have the functionality to display tasks on particular days -- at least I've never discovered how to do it. There is however an add-on 'Gantt View' that might do what you want. Judging from the screenshots it appears to display tasks as well as events on a calendar view (though not the normal Lightning calendar). Might be worth a look. Alternatively you could create an additional calendar -- i.e. have one for events and another for tasks -- both of them displaying in the normal Lightning day / week / month view. You could have them different colours if you want. In the 'tasks' calendar you would enter tasks as untimed (= all day) events. You wouldn't have all the functionality of the Tasks list (e.g. task priority, how many days until due etc.) but maybe that doesn't matter to you anyway. Personally I prefer to manage my tasks in a list but your needs are different.