did anyone file a lawsuit against them?
No. The brothers had filed a lawsuit against Glenn Curtiss and Louis Paulhan.
Wright brothers
Curtiss refused to pay license fees to the Wrights and sold an airplane equipped with ailerons to the Aeronautic Society of New York in 1909. The Wrights filed a lawsuit, beginning a years-long legal conflict.
who is credited with performing the first heavier-than-air flight The Wright brothers—Orville  and Wilbur Wright where did they spend their childhood? They lived in twelve places before finally settling down in Dayton. when did they make their first aircraft? The brothers flew the glider in the early autumn of 1900. which country do they belong to? The United States of America
wiki:5418132
Wright brothers [SEP] Lawsuits begin
Curtiss refused to pay license fees to the Wrights and sold an airplane equipped with ailerons to the Aeronautic Society of New York in 1909. The Wrights filed a lawsuit, beginning a years-long legal conflict. They also sued foreign aviators who flew at U.S. exhibitions, including the leading French aviator Louis Paulhan. The Curtiss people derisively suggested that if someone jumped in the air and waved his arms, the Wrights would sue.