Retrieval approaches that score documents based on learned dense vectors (i.e., dense retrieval) rather than lexical signals (i.e., conventional retrieval) are increasingly popular. Their ability to identify related documents that do not necessarily contain the same terms as those appearing in the user's query (thereby improving recall) is one of their key advantages. However, to actually achieve these gains, dense retrieval approaches typically require an exhaustive search over the document collection, making them considerably more expensive at query-time than conventional lexical approaches. Several techniques aim to reduce this computational overhead by approximating the results of a full dense retriever. Although these approaches reasonably approximate the top results, they suffer in terms of recall -- one of the key advantages of dense retrieval. We introduce 'LADR' (Lexically-Accelerated Dense Retrieval), a simple-yet-effective approach that improves the efficiency of existing dense retrieval models without compromising on retrieval effectiveness. LADR uses lexical retrieval techniques to seed a dense retrieval exploration that uses a document proximity graph. We explore two variants of LADR: a proactive approach that expands the search space to the neighbors of all seed documents, and an adaptive approach that selectively searches the documents with the highest estimated relevance in an iterative fashion. Through extensive experiments across a variety of dense retrieval models, we find that LADR establishes a new dense retrieval effectiveness-efficiency Pareto frontier among approximate k nearest neighbor techniques. Further, we find that when tuned to take around 8ms per query in retrieval latency on our hardware, LADR consistently achieves both precision and recall that are on par with an exhaustive search on standard benchmarks.