For the sake of completeness, there was HTML5 API called WebSQL which got deprecated before it went official, and some browsers still support it (and they even use SQlite internally for that).
It's not possible to load local *.db files though, so you'll need to export your database tables as JSON (or CSV), load and parse it using custom JS and use resulting objects to get monsters' stats. If you really have a lot of complicated SQL queries you really want to reuse, you probably can achieve that by putting retrieved data into WebSQL and applying those queries, but then again, it will not work in all browsers.