Probably not in most cases. But, as with many things in tax law (US Title 26), the true answer is that "it depends."
To that end, I'm attaching a pair of links to published articles that discuss this answer in some depth (both are written by lawyers experienced in this area) that should help explain, in detail, the various rules involved from a practical standpoint. Basically, they tell you when, as an attorney, you should be sending or receiving a Form 1099. As a practicing CPA, I would agree with their joint analysis. Here are those links:
http://www.woodllp.com/Publications/Articles/pdf/IRS_Form_1099_Ten.pdf
http://blog.sfbar.org/2015/04/02/to-1099-or-not-to-1099-proper-reporting-of-client-settlements/
Thanks for asking this important question.