The Tasks navigation menu item in Lightning Experience only includes the My Tasks, Today, All Overdue, Completed Within Last 7 Days, and Delegated task lists. All other task lists, including custom lists aren’t available.
The Calendar navigation menu item displays only a day view or a week view. The month or activity list views aren't available.
As a workaround, Lightning users may choose to leverage reports to view events and tasks.
Consider creating or promoting the existing Idea, List View Controls for Tasks tab in LEX so that we may see additional activity list view features added to Lightning Experience and Salesforce with a future release.
Productivity Features: What’s Not in Lightning Experience
Data Access and Views: What’s Not in Lightning Experience
Considerations for Using Tasks in Lightning Experience
Considerations for Using Events and Calendars in Lightning Experience
Calendar Views in Lightning Experience
Create a List View in Lightning Experience