1863, American English, from lobby (n.) in the political sense + -ist.
[A] strong lobbyist will permit himself to lose heavily at the poker-table, under the assumption that the great Congressman who wins the stake will look leniently upon the little appropriation he means to ask for. [George A. Townsend, "Events at the National Capital and the Campaign of 1876," Hartford, Conn., 1876]