We consider a single-job model lot streaming problem in two-machine flow shops with speed scaling, in which the job can be splitted into n consistent sublots, and each sublot can be processed at varying continuous speeds on each machine. The aim is to find an optimal schedule that determines both the sizes and the processing speeds of sublots so that the job can be finished before a given deadline and the total energy consumption is minimized. To solve this problem, we investigate the structural properties of the optimal schedules and show that it can be obtained within a no-wait environment. Then, we show that the problem is in fact a convex optimization problem, and can be solved by existing convex programming techniques.