You are correct! Lewis gun developed by BSA in England.
Colonel I.N. Lewis USA was the designer of the Lewis LMG. There is a good history of it in "Hatcher's Notebook".
It is a more successful design than it is credited to be, used by several armies by many countries on the ground and in the air.
After failed tests chambered in .30-'06 before WWI, Lewis submitted the gun to the British where it faired much better with the .303 British rimmed cartridge.
The Lewis guns employed by General Pershing in his pursuit of Pancho Villa were part of a purchase of 350 guns from the Savage Arms Co. Eventually, Savage worked out the bugs with the .30-'06 chambering and the Army ordered 2500 as of May, 1917. The Navy and Marines got 9270.
A stripped and lightened version for aircraft use was developed and the Army purchased 47,000.