Let's see what cls action is doing on Task. Whenever you click on it, It opens the edit page of the Task with status default to Close. Coming to Lightning, The way it is working is little changed. How?
If you are using Activity standard Component, it shows open activities as well as closed one in a different section. If you can see in below image, A checkbox just before the task name appears, also all the record level action are accessible via this component itself.
If you click on the checkbox, it will close the task.
If you click on Change status, It will allow you to close. It will open a popup to make a change in the status field. You can predefine the value to complete.
Even, Edit option is allowing you to change the status of the Task.
Read this too:- Check Tasks Off Your List with a Click