The drowning lawyer (or lawyers) joke has been one of the most popular of lawyer jokes. A simple form was cited in print in 1984: “‘Know how to save a drowning lawyer?’—‘No.’—‘Good.’”

“Q. How do you save five drowning lawyers? A. Who cares?” wa cited in print in 1993. “Q. How do you keep a lawyer from drowning? A. Take your foot off his/her head” was also cited in 1993.

“Q. How do you stop a lawyer from drowning? A. Shoot him before he hits the water” was cited in 1997.

Another drowning lawyer joke is, “What do you throw to a drowning lawyer? His partners.”
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Google Books
Curves of Pursuit
By Thomas Farber
New York, NY: Putnam
1984
Pg. 156:
“Know how to save a drowning lawyer?”
“No.”
“Good.”

Google Groups: aus.jokes
Insurance/Lawyer jokes wanted.
David Shanahan
5/18/93
(...)-
My favourite lawyer jokes -

1) Q. How do you save five drowning lawyers?
A. Who cares?

Derek Foster
5/25/93
(...)
How do you keep a lawyer from drowning?
Take your foot off his/her head..

Google Groups: rec.humor
What?No lawyer jokes? 
Anthony H Schroeder
9/19/93
(...)
Q:  Do you know how to save a drowning laywer?
A1: Take your foot off his head.
A2: No.
Good!

Google Groups: rec.humor
Some tasteless lawyer jokes
David Isaacs
12/4/94
(...)
Q: Do you know how to save a drowning lawyer?
A1: Take your foot off his head.
A2: No ... GOOD!

Google Books
The Joke’s On… Lawyers
By Stan D. Ross and Ysaiah Ross
Sydney: The Federation Press Pty Ltd
1996
Pg. 92:
Q: Do you know how to save a drowning lawyer?
Al: Take your foot off his head.
A2: No? Good!

Google Groups: nebr.humor
MORE Lawyer Jokes
Bluewasp
5/22/97
(...)
Do you know how to save a drowning lawyer?
A1: Take your foot off his head.
A2: No.? Good!

How do you stop a lawyer from drowning?
Shoot him before he hits the water.

Google Books
8 September 1997, New York magazine, pg. 79, col. 3 ad:
CARL: How do you save a lawyer from drowning?
DYLAN MCDERMOTT: How?
LEON: Take your foot off his head.
(ABC television.—ed.)

Google News Archive
17 October 2001, New Straits Times (Malaysia), “Short Lawyer Jokes,” Life & Times sec., pg. 8, col. 2:
Q. How do you save five drowning lawyers?
A. Who cares?

Q. How do you stop a lawyer from drowning?
A1. Shoot him before he hits the water.
A2. Take your foot off his head.

Twitter
GET LOLIFIED!
‏@TheLOLWorld
JOKE: How do you save a drowning lawyer?
1. Take your foot off his head.
2. Shoot him before he hits the water. http://ift.tt/1fTnxru
3:53 AM - 2 Jul 2014