Object-goal navigation has made substantial progress in semantic perception and exploration, yet persistent memory for multi-object navigation and cross-floor navigation are still commonly addressed separately. We present LifelongCrossNav, a framework for sequential multi-object ObjectNav in unknown multi-floor indoor environments. Within each episode, the agent receives an ordered sequence of object-goal queries while continuously maintaining a shared sparse 3D semantic voxel memory. This memory incrementally accumulates geometric structure, traversability states, and vision-language features, allowing subsequent object-goal queries to retrieve previously acquired scene information without rebuilding the map. To support persistent search across floors, LifelongCrossNav combines support-aware 3D traversability mapping, stair-specific perception, and direction-aware stair traversal. A unified navigation policy coordinates same-floor frontier exploration, live and historical point-of-interest retrieval, stair navigation, and target-object search and approach. We further introduce HM3D-MFMON, a benchmark for sequential Multi-Floor Multi-Object Navigation built on HM3D scenes, including a dedicated subset in which completing the full sequence of object-goal subtasks requires at least one floor transition. Experimental results show that LifelongCrossNav consistently outperforms a representative planar persistent semantic-map baseline on HM3D-MFMON, demonstrating that persistent 3D semantic memory and cross-floor traversability modeling effectively support sequential multi-object navigation in multi-floor environments. Project page: https://flageval-baai.github.io/LifelongCrossNavPage.

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