Vector databases increasingly enforce role-based access control, where each top-k approximate nearest neighbor query must return only vectors the querying role is authorized to access. Two extremes bracket the design space. A single global index built over all vectors avoids duplication but wastes search effort on unauthorized vectors and degrades recall, while an oracle index, built with all authorized vectors to the query roles, searches only authorized vectors but duplicates every shared vector between roles or queries. We present Veda and its efficient variant EffVeda, two indexing strategies built on an access-aware lattice to address access control in vector databases. The methods first partitions the dataset into disjoint data blocks by role combination, then leverage the structure of the access-aware lattice to apply copy and merge operations to group co-accessed blocks under a user-specified storage budget. Large nodes in the lattice are then indexed with HNSW, while small nodes are retained for linear scan. To facilitate query processing on the lattice, our methods construct a query plan that selects the minimal set of nodes that covers all authorized data for each role. At query time, coordinated search first queries pure (authorized-only) nodes to populate a global top-k heap, then leverages the resulting distance bound of the k-th data in the heap to prune exploration on impure nodes. Evaluations show that our methods deliver higher throughput at high recall while closely tracking the storage budget.