In an idea posted a year ago - https://success.salesforce.com/ideaView?id=08730000000LjHIAA0
- it was argued that Lightning Experience should be able to show archived activities. The idea has been marked as "Delivered in Winter '18". And while that is technically true, the delivered functionality isn't exactly what I had expected.
Even though the archived tasks can now be seen in the related list, when doing mouse-over, or trying to click the actual task, you get an error message:
'ooks like there's a problem.
You do not have the level of access necessary to perform the operation you requested. Please contact the owner of the record or your administrator if access is necessary.
It is also described in this Question: https://success.salesforce.com/answers?id=9063A000000pIg6QAE
It means that the user can see that there is a historic task, but it is not possible to view the details of each task, including description etc. I would appreciate if you could replicate the behaviour of Classic in this regard.