The purpose of this study was to determine if estimated breeding value (EBV) of an animal’s sire and or the animal’s nutrition affected the structure of its M. longissimus thoracis et lumborum (LL) and, hence, the eating quality of meat derived from its carcass. Lambs were chosen based on the EBV of their sires in terms of post-weaning live weight (PWWT), post weaning fat at the C-site (PFAT), and post-weaning eye muscle depth (PEMD). Morphometric techniques were used to characterise muscle structure in terms of the distribution of intramuscular connective tissue; the variables together are called fascicular structure. Perimysial seam thickness and fascicular width were both influenced by sire estimated breeding values for PWWT, PFAT, and PEMD. Variation in fascicular structure was associated with an interaction between PEMD-EBV and PFAT-EBV of the sire. Fascicular width decreased with increased PEMD-EBV and increased with PFAT-EBV, but was not affected by PWWT-EBV. When the total seam thickness was adjusted to a common fascicular width, the lambs on a low plane of nutrition had relatively more intramuscular connective tissue than those on a high plane. The total seam thickness was negatively associated with PFAT-EBV and positively associated with PEMD-EBV. Warner Bratzler shear (WBS) peak force (PF) and initial yield were not associated with differences in sire EBV. The residual WBS shear force, peak force minus initial yield (PFIY), and compression values were negatively associated with nutrition but were positively associated with PWWT-EBV and PEMD-EBV of the sires. These latter 2 effects were moderated by nutrition. The data support the hypothesis that morphological characteristics of perimysium are genetically determined and nutritionally responsive. Variance in morphology accounted for some variance in the biophysical attributes of meat and may help explain why sheep with high muscling potential have tougher meat.