When you enable Lightning, the ability to add activities is not automatically added to page layouts (e.g. Log a Call, New Task, etc.). You have to edit each page layout, choose to edit the Salesforce Mobile and Lightning Experience Actions section, and then add the actions.
How do I add a new activity in Salesforce?
In Salesforce.com, click Setup. In the Build section, click Customize > Activities. Make sure you click just the “Activities” link–don’t click the drop-down beneath “Activities”. On the Activities page, click Add a custom field to activities.
How do I add a task to an activity in Salesforce?
Select Create New Task from the sidebar or click the New Task button on the Open Activities related list of a record, as shown. Either way, the result is the same. A New Task page appears. When creating tasks, go to the record that the task is most directly related to before adding the task.