We address the flow shop scheduling problem with two machines and time delays. We dispose of a set J={1,2,...,n} of n jobs that must be executed without preemption on two machines M1 and M2, which can only handle one operation at a time. Each job j has two operations. The first operation must be executed during p(1,j) time units on M1. Then, lj time units are needed to transport job j to M2, where the second operation has to be executed during p(2,j) time units. The objective is to find a feasible schedule on the two machines that minimizes the completion time of the last scheduled job on M2. This problem is NP-hard in the strong sense even with unit-time operations. We present a comprehensive theoretical analysis of the different lower bounds of the literature and we propose new relaxation schemes. Then, we elucidate dominance relationships between them. Moreover, we investigate a linear programming-based lower bound that includes the implementation of a new dominance rule and a valid inequality. Finally, we present the result of an extensive computational study that was carried out on a set of 480 instances including new hard instances. Our new relaxation schemes outperform the state of the art lower bounds.