“How can you tell when a politician is lying?” is the start of an old joke. The answer: “His lips are moving.”
   
“How can you tell when a lawyer is lying?” is the most familiar form of the joke today. Many other people and professions have been substituted.
 
The earliest form of the joke (cited in print in 1935) appears to be a wife who was asked: “How can you tell when your husband is lying?” The politician version dates from at least 1956.
 
“How can you tell if a violin is out of tune?”/“The bow is moving” is a related joke. “How do you know when a website is lying? It ends in dot gov” is a related saying about government.
   
   
8 February 1935, Angola (IN) Herald, “This Week’s Best Stories and Witticisms,” pg. 4, col. 5:
Can you tell when your husband is lying?
 
Yes; if his lips are moving he is.
 
10 April 1935, Amarillo (TX) Globe, “The Tactless Texan,” pg. 2, col. 2:
Some people were talking about a new machine known as the lie detector.
 
“I don’t need such a machine to tell me when my husband is lying,” a smart old country girl remarked.
 
“How’s that” she was asked.
 
“All I have to do is look at his lips.”
 
“How can you tell by them.”
 
“Well, if they’re moving he’s lying.”
   
15 June 1935, Denton (MD) Journal, ‘The Featherheads” by Osborne (comic strip), pg. 4, col. 2:
Panel One:
WIFE: WELL, WHERE HAVE YOU BEEN SO LATE?
HUSBAND: WELL—ER—YOU SEE—
Panel Two:
WIFE: BEFORE YOU START—I MIGHT AS WELL TELL YOU I CAN TELL IF YOU’RE LYING!
HUSBAND: HUH! I WOULDN’T LIE TO YOU, DARLING—BUT HOW COULD YOU TELL IF I DID?
Panel Three:
WIFE:  BY LOOKING AT YOUR FACE—IF YOUR LIPS ARE MOVING—YOU’RE LYING!!
Panel Four:
WIFE:  WELL—GO ON WITH YOUR STORY.
Panel Five:
DUCK/NARRATOR: IF YOUR STORY IS DOUBTFUL—LET IT LIE.
     
6 June 1939, Lubbock (TX) Evening Journal, pg. 6, col. 1:
A couple of wives were gabbing about their husbands.
 
“How,” asked Mrs. Smith, “can you tell when your husband is lying?”
 
“Humph!” snorted Mrs. Jones, “if his lips are moving, he is!”
 
Google Books
Thesaurus of Humor
By Mildred Meiers and Jack Knapp
Edition: 11
New York, NY: Crown Publishers
1940
Pg. 165:
Can you tell by your husband’s face if he’s lying?
Yes. If his lips are moving, he is.
 
18 April 1948, Chicago (IL) Daily Tribune, “Radio Gag Bag” culled by Larry Wolters, pg. E21, cols. 2-3:
Beulah: How can I tell whether Bill’s lying?
Oriole: O, that’s easy.
Beulah: It is?
Oriole: Sure, if his lips are moving, he’s lying!
   
5 September 1956, Charleston (WV) Daily Mail, “Buick Topics” by T. M. Gardner, pg. 12, col. 1:
We recently heard a story about a young man who had become of voting age and was taking his obligation and responsibility very seriously. He had been listening to talks by the various candidates in their public, television and radio appearances. It was all rather confusing and contradicting to this young man. So he consulted his Father for advice on how he could determine when these candidates were lying. The Father said, “Son, that’s easy. If their lips are moving, they’re lying.”
 
Google News Archive
21 October 1957, Milwaukee (WI) Sentinel, part 1, pg. 19, col. 2:
Overheard: “I can always tell when my husband’s lying. I just watch his face to see if his lips are moving.”
   
9 July 1986, Los Angeles (CA) Times, Metro, section 1, pg. 3:
How can you tell if a lawyer is lying?
His lips are moving.
   
Sports Illustrated
March 27, 1989
Here Today, Gone Today
A coach may swear he’s staying, but who can believe him?
Rick Reilly
From now on, Rule No. 1 about college coaches is this: If their lips are moving, chances are they’re lying.