“Lute” (a musical instrument) shouldn’t be confused with “loot” (contraband, plunder), but there are jokes. This joke was printed in the Detroit (MI) Free Press on May 25, 1977:

“TODAY’S WORST JOKE: There was the guy who robbed a music store, made off with the lute.”

A different version (a musician robbing a bank) is this riddle, posted on the newsgroup alt.uk.penpals on January 4, 2000:

Q: What happened to the musician that robbed the bank?
A: He made off with the lute.


25 May 1977, Detroit (MI) Free Press, “The Town Crier” by Mark Beltaire, pg. 3A, col. 1:
TODAY’S WORST JOKE: There was the guy who robbed a music store, made off with the lute.

3 June 1994, Pittsburgh (PA) Post-Gazette, “Puzzle Solutions,” pg. B-11, col. 2:
Solution for previous Cryptoquip:
Very clever thief robbed music store downtown and made off with the lute.

Google Groups: alt.uk.penpals
Just for a laugh
Alan
1/4/00
(...)
What happened to the musician that robbed the bank?
He made off with the lute

Google Groups: alt.humor.puns
LSD GOES NUTZ was re: Why is ‘widdle’dougie ellis, so St00pid
Stan Kegel
3/10/01
(...)
44 What happened to the musician that robbed the bank?
He made off with the lute (By Scott Ryan) •

Google Groups: alt.humor.puns
Puns of the Weak 01/04/02
Stan Kegel
1/5/02
(...)
What happened to the musician that robbed the bank?
He made off with the lute (Cynthia MacGregor)

Google Groups: alt.humor.puns
Puns of the Weak 08-22-03
Stan Kegel
8/22/03
(...)
Heard about the musician who robbed the bank… He made off with the lute!
(Nick Grivas)

Twitter
Gadget Meistress
@joyctilton
RT @BlindFunk Heard about the musician that robbed the bank.... He made off with the lute!
11:38 PM - 19 Nov 2009

Twitter
PUNS
@omgthatspunny
Heard about the musician that robbed the bank...he made off with the lute! #punny
10:38 PM - 31 Aug 2011

Twitter
Martin Lewis
@MartinLewis96
A music store was robbed in town today. The theif made off with the lute.
11:39 AM - 4 Nov 2012

23 June 2013, Asheville (NC) Citizen-Times, “Doodle Zoo,” comics sec., pg. 2, col. 4:
A MUSICIAN ROBBED THE BANK. HE MADE OFF WITH THE LUTE!

Google Books
The Everything Big Book of Jokes:
Hundreds of the Shortest, Longest, Silliest, Smartest, Most Hilarious Jokes You’ve Ever Heard!
By Evan C Thomas
Avon, MA: Adams Media
2014
Pg. 121:
A MUSIC STORE WAS ROBBED last week. The robbers made off with the lute.

Google Books
The Best Joke Book (Period):
Hundreds of the Funniest, Silliest, Most Ridiculous Jokes Ever
By William Donohue
Avon, MA: Adams Media
2014
Pg. 81:
A music store was robbed last week. The robbers made off with the lute.

Reddit—Dadjokes
Posted by u/Ew0k5AN0nomi5 June 21, 2019
Did you hear about the robbery at the music store?!
The thief made off with the lute.