The agency has been briefed to encourage more consumers to opt for 100 per cent renewable energy. Good Energy predominantly supplies energy from wind and solar sources.
Helen Calcraft, a founding partner at Lucky Generals, said: "There is a clear determination at Good Energy to revolutionise the energy market, and make the world a better place.
"We set up Lucky Generals to work with people on a mission, and this is a mission we applaud and admire."
Calcraft set up Lucky Generals alongside former Dare and MBCD colleagues Danny Brooke-Taylor and Andy Nairn. The agency is based in Farringdon, London.