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Assembly job shop scheduling problem (AJSSP) is an extension of classical job shop scheduling problem (JSSP). AJSSP first starts with a JSSP and appends an assembly stage after job completion. In this paper, we extend Lot Streaming (LS) to AJSSP. Hence, the problem is divided into SP1: the determination of LS conditions for all lots and SP2: the scheduling of AJSSP after LS conditions have been determined. To solve the problem, we propose an innovative Genetic Algorithm (GA) approach. To investigate the impacts of LS on AJSSP, several system conditions are examined. To justify the GA, Particle Swarm Optimization (PSO) is the benchmarked method. Computational results suggest that equal size LS is the best strategy and GA outperforms PSO for all test problems. Some negative impacts of LS are the increase of work-in-process inventory and total setup cost if the objective is the minimization of total lateness cost.