A joke about someone drinking varnish was published in the Brooklyn (NY) Daily Eagle on April 7, 1938:
 
“Poor Joe! He died from drinking varnish.”
“At least he had a fine finish.”
 
“Did you hear about the guy who died after drinking a bottle of Varnish? He had a horrible end, but a lovely finish”—a popular form of the joke—was posted on Twitter on April 20, 2010.
 
           
7 April 1938, Brooklyn (NY) Daily Eagle, “Si and Smudgie” by Paddock Pete, pg. 18, col. 3:
“Poor Joe! He died from drinking varnish.”
“At least he had a fine finish.”
 
5 January 1945, The Daily Argus-Leader (Sioux Falls, SD), pg. 6, col. 7:
Thought for Today
Wall Street Journal
The guy who died from drinking varnish—certainly had a fine finish!
 
25 October 1949, Oakland (CA) Tribune, pg. 48, col. 8:
Newspapers tell of a man who died from drinking varnish. He certainly had a fine finish.—Florence (Ala.) Bulletin.
 
23 August 1959, Statesman (Salem, OR), “Valley Footnotes” by Mervin Jenkins, sec. 2, pg. 15, col. 1:
One of the many “stories” reported this week but never getting into print was about the man who died from drinking varnish. It was an awful sight, but a beautiful finish.
 
16 September 1984, Daily Record (Morristown, NJ), “Worst Verse” by Gyles Brandreth, YOU sec., pg. 13, col. 2:
Down the street his funeral goes
As sobs and wails diminish,
He died from drinking varnish,
But he had a lovely finish. 
     
Google Books
Shredded Wit
By Vernon K. McLellan
Eugene, OR: Harvest House Publishers
1988
Pg. 181:
He died through drinking varnish, But he had a lovely finish.
 
Google Groups: alt.test
test
.(JavaScript must be enabled to view this email address)
10/25/90
If anybody really is so bored to have read this test, here is a joke:
 
A man fell into a vat of varnish and died. Terrible end but a lovely finish!
   
Google Books
Spoken in Jest
By Gillian Bennett
Sheffield, UK: Sheffield Academic Press
1991
Pg. 291:
Drink varnish — It gives a lovely finish.
 
17 March 1991, Calgary (Alberta) Herald, “Ah to be sure, to be sure . . .” by Tom Hennessy, pg. A2:
Murphy gets a wire from Dublin: “Uncle Sean drank varnish by mistake. Had horrible death, but a lovely finish.”
       
Google Groups: alt.fan.pratchett
Scumble
Bernard M. Earp
7/8/99
In article .(JavaScript must be enabled to view this email address), Emma .(JavaScript must be enabled to view this email address) writes
>If scumble glaze is anything like a varnish, it probably does contain
>ethane, in which case it could (technically) get you pished.
 
“What he drank two pints of the stuff?”
“Yes it killed him. . . But he had a lovely finish”
 
23 January 2006, The Advertiser (Adelaide, Australia), “Summer fun for young” by Samela Harris, pg. 69:
Of course, they are all fresh to today’s young, even though many pass way over their heads: “My second husband drowned in a barrel of varnish. It was a terrible end, but he had a lovely finish.”
 
Twitter
Andrew Adshead‏
@Andrewnotmatt
R.I.P. uncle paddy, you died after drinking a bottle of varnish. A horrible death but a lovely finish…
9:37 AM - 24 Mar 2009
   
Twitter
Andy graham‏
@Andy_graham84
Did you hear about the guy who died after drinking a bottle of Varnish? He had a horrible end, but a lovely finish.
12:02 PM - 20 Apr 2010
     
Google Books
More Aussie Gags
By John Blackman
Sydney, Australia: Momentum
2012
Pg. ?:
Then there was the bloke who drank a bottle of varnish. Of course he died, but it was a lovely finish.
 
Reddit—Jokes
My grandfather drowned in varnish recently.
submitted November 3, 2012 by Tobahkiin
A horrible way to go, but a lovely finish.
   
Twitter
A friend of mine died recently
submitted December 8, 2016 by fatcatandgingy
A friend of mine died recently after drinking a gallon of varnish. It was a horrible end, but a lovely finish.
 
Reddit—Jokes
A friend of mine died recently after drinking a bottle of varnish…
submitted February 18, 2018 by patchy72
...It was a horrible end, but a lovely finish.