Lithium has several options to improve search relevancy.
First, do you have auto suggest turned on? It will provide search suggestions as users type their search.
can read about in this release note article here
It explains the spellcheck options, how to add words to custom dictionary and how to enable combinatorial search.
Combinatorial search might be the one to help you out here.
Lithium Community now supports combinatorial search. When combinatorial search is enabled and a user enters a multi-term search string, various combinations of the individual terms are used to conduct the search to generate the search results. Previously, all terms in the string needed to be matched before a result was shown. Now the search uses a fuzzier heuristic.
The search settings can be set by administrators in the search admin however the items mentioned in the release notes need to be tweaked from the back-end, through a support ticket.
Hope this helps you a bit.
... View more