If the pairs of entities you want to compare are already given in advance, and you are interested in the pair-wise scores, I don't think Lucene will give you any advantage. Just lookup the vectors in some key-value store and compute the similarity. Consider using a sparse vector representation for space and time efficiency.
If only one entity is given in advance, and you are more interested in a ranking like scenario, Lucene may be worth a try.
The right place to look at would be
org.apache.lucene.search.Similarity
you should be able to adapt it to your needs and set your version as default with
setDefault(Similarity similarity)
I would be careful with expectations for speed gains (w.r.t. iterating through all) however, as they largely depend on the sparsity (of the query) and the scoring function you choose to implement. Also note that Lucene uses a two-stage retrieval scheme, first boolean ("all of the AND terms contained? any of the OR terms?") then scoring what passes. While for tf.idf you lose nothing on the way for other scoring functions you might.
For more general approaches for efficient approximate nearest neighbor search it might be worthwhile to look into LSH:
http://en.wikipedia.org/wiki/Locality-sensitive_hashing