Will every believer receive a responsibility in Christ's kingdom?
Yes. As resurrected saints, every believer will receive an area of responsibility from God in Christ's kingdom. The parable of the talents shows rewards vary, with the faithful servant ruling over ten cities. The exact manner remains unexplained, but believers work for varying amounts of responsibility in that kingdom economy.
Les teaches that resurrected saints will not be part of the flesh-and-blood population filling the earth during the kingdom. Instead, they will interface with them from a place of authority. God will give every believer an area of responsibility, and beyond that he cannot explain it. He bases this on the account of the talents, where the servant who gained ten talents was told he would rule over ten cities. Thus the rewards of the believer will be various amounts of responsibility in the kingdom economy. How it will be done is unknown, but that is what believers work for.