In this study, the shear-induced lamellar alignment of a thin-film ABA triblock copolymer melt was achieved via a non-equilibrium coarse-grained molecular dynamics simulation. The ABA triblock copolymer system displayed a slightly different phase behavior under different shear conditions compared to the AB diblock copolymer system. Unlike previous studies that only considered the wall velocity, the Flory-Huggins parameter was considered in our study as a factor that determines lamellar alignment. Pre-aligned lamellae and randomly mixed polymers were used as the initial states for the shear simulation to compare the shear-induced lamellar alignment on each. The two initial conditions displayed different alignment behaviors; specifically, in the pre-aligned lamellae, a tilted structure was observed when the system was not aligned in the shear direction. To explain the difference between the tilted and realigned structures, the potential energy over the simulation time, polymer dynamics from the Van Hove correlation function, and the directional order parameter were investigated. It was inferred that a tilted structure is induced by the energy barrier of realignment originating from the restricted movement of the local polymer chains. Once they cross the energy barrier, block copolymers tend to align in the shear direction to attain energy stabilization through the polymer flow.