The directed assembly of lamella-forming copolymer systems on substrates chemically patterned with rough stripes has been studied using a Helfrich-type, phenomenological theory and Single-Chain-in-Mean-Field (SCMF) simulations. The stripe period matches that of the lamellar spacing in the bulk. The effect of the line edge roughness (LER) of the substrate pattern on the microphase-separated morphology was investigated considering two generic types of substrate LER with a single characteristic wavelength imposed on the edges of the stripes: undulation and peristaltic LER. In both cases, the domain interfaces are pinned to the rough stripe boundary at the substrate and, thus, are deformed. We study how this deformation decays as a function of the distance from the substrate. The simple theory and the SCMF simulations demonstrate that one of the basic factors determining the decay of the roughness transferred into the self-assembled morphology is the characteristic LER wavelength of the substrate pattern; i.e., the distance over which the roughness propagates away from the substrate increases with wavelength. However, both approaches reveal that, for a quantitative understanding of the consequences of substrate LER, it is important to consider the interplay of the pattern wavelength with the other characteristic length scales of the system, such as the film thickness and the bulk lamellar spacing. For instance, in thin films, the induced deformation of the lamellar interface decays slower with distance from the patterned surface than in thicker films. It is shown that the phenomenological theory can capture many of the same qualitative results as the SCMF simulations for copolymer assembly on substrate patterns with LER, but, at the same time, is limited by an incomplete description of the constraints on the polymer chain conformations imposed by the substrate.