Lot streaming is a strategy of splitting a production lot into several sublots so that completed sublots can be transferred to a downstream machine before the entire lot has been completely processed at a current machine. Such a strategy increases the velocity of material flow through a system. However, an increase in the number of transfers between stages also increases material handling cost. In this paper, we address the problem of minimizing a weighted sum of the makespan and handling costs when multiple lots are produced in an assembly system consisting of s suppliers in the first stage and a single assembly machine in the second stage. We exploit a relationship between an optimal solution for this problem and that for a related single-lot, two-machine makespan minimization problem in developing a polynomial-time algorithm to obtain the optimal number and sizes of sublots for each lot when a sequence for processing the lots on the assembly machine is given. We also provide novel integer programming formulations to simultaneously determine an optimal production sequence for the lots and the number of sublots and sublot sizes for each lot, and present a polynomial-time method to obtain valid inequalities for this problem. Experimental results are presented to demonstrate the effectiveness of this formulation over the traditional linear-ordering-based formulations.