You can use a Lightning record page to replace the view for a single SObject in the Lightning Record Page option in setup.
How do I do that for the list view?
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You can't override the list view separately in Lightning because it's fused with the object home page, the Tab, which is overrideable.
From the Lightning Components Developer Guide:
Lightning Experience and the Salesforce mobile app combine the Tab and List actions into one action, Object Home. However, Object Home is reached via the Tab action in Lightning Experience, and the List action in the Salesforce mobile app. Finally, the Salesforce mobile app has a unique Search action (reached via Tab). (Yes, it’s a bit awkward and complicated.)
Yes, it is possible to override the listview in the lightning record home page.
The trick is to override the listview. You can currently only override the listview with a visualforce page. The override will apply in both classic and lightning. You can use Lightning Out in the VF page if you want to render a lightning component.
The ListOverride Visualforce page:
<apex:page standardController="Case" recordSetVar="X" >