Association mining seems to give good results for retrieving related terms in text corpora. There are several works on this topic including wel
You can export a Lucene (or Solr) index to Mahout, and then use Latent Dirichlet Allocation. If LDA is not close enough to LSA for your needs, you can just take the correlation matrix from Mahout, and then use Mahout to take the singular value decomposition.
I don't know of any LSA components for Solr.