Fatalistic mentality? It's not fatalism to make a decision to take a risk.
Lottery tickets are a means to have an opportunity of a great payoff, albeit with a very low chance of success. It seems to me that the purchase of lottery tickets is a signal of pessimism regarding the potential of reaching one's dreams via perseverence and non-gambling methods--and that is not fatalism, per se.
This is exactly the phenomenon Nisbet was describing. Fatalism is the belief that fate, rather than effort or character, is responsible for outcomes.