George and Lennie may have a dream and desires, but they are not living the American dream. George and Lennie's dream is not to live under someone else. However, under circumstances their independence is unrealistic, making their dream unattainable.
In order to survive and live, George and Lennie have to settle for living and working under someone else. They lack the initiative or power to fulfil their dream of living on the farm. George and Lennie lack the luxury to choose how to live. to live.
The American Dream was attainable, up until the point where Lennie kills with Curley’s