We consider the flow shop problem with two machines and time delays with respect to the makespan, i.e., the maximum completion time. We recall the lower bounds of the literature and we propose new relaxation schemes. Moreover, we investigate a linear programming-based lower bound that includes the implementation of a new dominance rule and a valid inequality. A computational study that was carried out on a set of 480 instances including new hard ones shows that our new relaxation schemes outperform the state of the art lower bounds.