One of the key structural proteins in the eukaryotic cell nucleus is lamin. Lamins can assemble into a two-dimensional protein meshwork at the nuclear periphery, known as the nuclear lamina, which provides rigidity and shape to the nucleus. Mutations in lamin proteins that alter the structure of the nuclear lamina underlie laminopathic diseases, including Hutchinson–Gilford Progeria Syndrome (HGPS). Experiments have shown that, compared to healthy cells, lamin supramolecular structures (e.g., protofilaments) assemble into a thicker lamina in HGPS, where they form highly stable nematic microdomains at the nuclear periphery, reminiscent of liquid crystals. This significantly alters the morphological and mechanical properties of the nucleus. In this study, we investigate the aggregation of lamin fibrous structures and their dissociation kinetics from the nuclear periphery by modeling them as coarse-grained, rod-like polymer chains confined within a rigid spherical shell. Our model reproduces the formation of multidirectional nematic domains at the nuclear surface and the reduced lamin dissociation observed in HGPS nuclei by adjusting lamin concentration, lamin–lamin (head–tail), and lamin–shell association strengths. While nematic phase formation requires relatively strong lamin–shell affinity under any non-vanishing inter-lamin attraction, the thickness of the lamina layer is primarily controlled by the head–tail association strength in the model. Furthermore, the unbinding kinetics of lamin chains from the lamina exhibit a concentration-dependent facilitated dissociation, suppressed by strong intra-lamin interactions, reminiscent of diseased nuclei. Overall, our calculations reveal the physical mechanisms by which mutations affecting native lamin interactions and concentration could lead to an abnormal nuclear lamina in laminopathic diseases.