How can we enable the Lightning UI within Marketing Cloud? I tried to find any settings in Admin setting but can't find anything.
Lightning's a CRM/Force.com thing. In Marketing Cloud, it's a buzzword that's loosely used to refer to incremental updates to the UI that pinch some of the styling of "Lightning Design System" - the CSS used by some CRM users.
There's no button to press or checkbox to tick. Bot you'll see certain parts of Marketing Cloud that have been spruced up "Lightning Style".