Rather than a random lottery it would be better if it was at least performance based. Sort of like the United 100 program, where employees are nominated by their peers for going above and beyond. Give the winners of that some substantial bonus money, and maybe that would be incentive enough to try harder on a daily basis.
A lottery is just a slap in the face. Especially once the first winners are announced and there inevitably ends up being some lazy POS who doesn't do anything beyond the bare minimum who wins, creating even more disdain and division. Bad all around.