Listed below are five Across answers to a crossword puzzle titled PERJURY.  Can you come up with the construction idea the author used in five related Across answers to satisfy the theme of the puzzle as suggested by the title?

CAN'T DO A THING
MY THROAT HURTS
SEMI-PRO ATHLETES
SHOWBOAT HOTEL
THE ROAD TO ATHENS

HINTS:
#1: Each answer above contains the same hidden word. 
#2: The five related answers are:
BELIE
LIE OVER
PURLIEU
LIENS
FLIED OUT

Answer:

The constructor (Joe DiPietro) arranged the five related answers so that the word LIE appeared directly under the word OATH, which is hidden in each of the first five answers.  This construction visually satisfied the theme PERJURY - LIE UNDER OATH.

Credit: NY Times Crossword
Joe DiPietro
PERJURY