I'm running sqlite and activerecord from shoes. And ferret and acts_as_ferret actually. I have no idea if this is good or proper but I downloaded a new sqlite3.dll from http://www.sqlite.org/sqlitedll-3_5_4.zip and then stuck the dll in the same directory as shoes.exe. Everything works for me with that situation. Perhaps the sqlite3.dll bundled with shoes isn't current? On my system the one bundled with shoes is 212 KB while the one downloaded is 420 KB. Hope that helps.
-Garret Buell
