Is it necessary to install vapor barriers in a basement, either on walls or floors when using pressure treated lumber?

Yes

If Your Closing The Basement In To Make A Room Then Yes, You'll Need To Seal The Block Wall Attach Your Treated 3/4 Boards Or You Can Use Untreaded Studs But Keep Them Off The Wall An 1" The Bottom Plate Will Still Need To Be Treated. After This A 40 Mill Clear Plastic Is Used And Just Stapel That Up.
Hope This Helps , Nichols Trim And Carpentry

Is it good to install vapor barriers on above ground exterior walls?