If you're looking to access SQLite databases on the browser (ie. client side) you'll need your browser to support it. You can do it with SpiderApe http://spiderape.sourceforge.net/plugins/sqlite/ which assumes that browser is Mozilla based (ie. with SQLite support). You'll still need to allow access to the underlying libraries ( http://www.mozilla.org/projects/security/components/signed-scripts.html )
If you're looking for serverside access from Javascript programs to SQLite databases there are several options: JSDB is one http://www.jsdb.org/ ; JSEXT another http://jsext.sourceforge.net/ ; and jslibs another http://code.google.com/p/jslibs/
-- MV