Structured data analysis typically requires performing multi-attribute queries over tabular data, making efficient multi-dimensional indexes key support for database systems. However, existing multi-dimensional indexing methods face limitations in high-dimensional scenarios. Traditional multi-dimensional indexing methods partition data uniformly based on data distribution but lack the awareness of query features, resulting in limited filtering effectiveness. In contrast, although existing learned multi-dimensional indexes introduce query-awareness, they often produce highly unbalanced partitions, thereby resulting in some oversized partitions and substantially increased scanning costs. To this end, this study proposes LA-tree, a novel learned tree-based multi-dimensional index that balances both data distribution and query workload awareness. In the offline construction phase, LA-tree formulates the selection of partitioning dimensions at each node as an optimization problem of minimizing the overall scan ratio of the query workload, and puts forward a hierarchical greedy search algorithm to achieve the unity of uniform partitioning and query-awareness. In the online query phase, the lightweight linear model and piecewise linear model are introduced to transform traditional numerical comparisons to fast mapping computations, thereby reducing filtering latency while ensuring the completeness of query results. In dynamic settings, an adaptive incremental update mechanism based on scan volume monitoring is proposed to efficiently adapt to changes in data and query workloads via local subtree reconstruction, thereby avoiding the high cost of rebuilding the entire index. Experimental results demonstrate that LA-tree outperforms existing methods on multiple real-world and benchmark datasets. In static settings, the query time is reduced by an average of 52% compared with the optimal benchmark method, while in dynamic settings, the update costs are reduced by 97% compared with the reconstruction methods. Additionally, low query latency and lightweight index scale are maintained.