Thanks for the link, I've been hunting around everywhere looking for a cross platform solution.
In a sibling comment I mentioned the fact that most languages compile to Javascript, the primary benefit being able to share code across client and server. So, if you've got a query DSL on the server that hooks into an SQL database you can use the same code on the client, hooking into an SQL database on the frontend.
All of the IndexedDb wrappers I've seen do essentially their own thing; in Lovefield's case, "The difference is that Lovefield does not accept raw SQL statements; instead, it has a builder-pattern API to build queries", which means it's effectively a client-side only solution if pure SQL is the output target of your query DSL.
not exactly sqlite-lite, but it's sqlish and it's build on top of IDB: https://github.com/google/lovefield