if I purchase either of the new Lunar Screen Borders, will I be able to "wear" them only on the given champion's loading screen? for example Nasus's Border only on Nasus,etc.
Yes, the Lunar Screen Borders are for situations when you are playing that champion with that one skin. In this case, when you play Lux, Nasus, or Warwick with their Lunar Revel skin, you will have the special border along with the splash art in the loading screen.