Search systems are increasingly used for reasoning-intensive queries, where what makes a document relevant requires understanding or reasoning over the query-document relation rather than relying on surface vocabulary or topical similarity. The standard recipe - a cheap embedding-based retriever followed by an LLM verifier - works only when the embedding model places the right documents in its top-k, an assumption that recent reasoning-intensive IR benchmarks show often fails to hold even for SOTA embedding models. Recent query-side fixes such as query rewriting and agentic loops keep the LLM upstream of the cheap retriever and remain brittle to the embedder's failures and to the LLM's ability to rewrite the query from its parametric knowledge. In this paper, we explore a different paradigm - LLM-guided hierarchical search - in which an LLM interacts with the corpus directly via a hierarchically navigable search index, with no embedding model in the loop at search time. We propose LATTICE, an instantiation with two technical contributions: (i) a top-down LLM-guided construction of the search index using LLM judgements over multi-level document summaries, and (ii) a calibrated, path-aggregated LLM-guided traversal that mitigates noisy, slate-dependent LLM scores via cross-branch reference nodes. On the reasoning-intensive BRIGHT benchmark, base LATTICE with a single off-the-shelf LLM achieves 46.7 nDCG@10 - matching the best fine-tuned ensemble baseline overall - and a lightweight ensemble LATTICE++ that fuses LATTICE with cheap retrieval reaches 49.1 nDCG@10. A controlled same-LLM comparison against sliding-window reranking shows reranking offers a better tradeoff at low token budgets, but LATTICE converges to a higher asymptote after a moderate budget. LATTICE also works with open-weight LLMs and remains competitive on traditional IR benchmarks (NQ, SciFact, SciDocs).