Generating piano accompaniments in the symbolic music domain is a challenging task that requires producing a complete piece of piano music from given melody and chord constraints, such as those provided by a lead sheet. In this paper, we propose a discrete diffusion-based piano accompaniment generation model, D3PIA, leveraging local alignment between lead sheet and accompaniment in piano-roll representation. D3PIA incorporates Neighborhood Attention (NA) to both encode the lead sheet and condition it for predicting note states in the piano accompaniment. This design enhances local contextual modeling by efficiently attending to nearby melody and chord conditions. We evaluate our model using the POP909 dataset, a widely used benchmark for piano accompaniment generation. Objective evaluation results demonstrate that D3PIA preserves chord conditions more faithfully compared to continuous diffusion-based and Transformer-based baselines. Furthermore, a subjective listening test indicates that D3PIA generates more musically coherent accompaniments than the comparison models.