There are several AIR/SQLite frameworks around, but I don't recall seeing anything that would automagically sync a server database to a local database.

I've had good luck with Paul Robertson's framework:

https://github.com/probertson/air-sqlite/network

It has a bunch of nice features which take care of the grunt work -- transactions (they're really important for optimizing performance), pooling -- and leave you with mostly just having to write your SQL queries and callback functions. I used Nate Ross's fork of this project and made a few very small tweaks. Paul was recently re-hired by Adobe, so he might be around somewhere to answer questions. I found his blog (http://probertson.com/) to be the best source for SQLite and AIR info.

You'll need a way to administer your local db, preferably one that knows about the proprietary features Adobe added to the AIR version of SQLite. The pickings are slim in this area. I've been mainly using Lita (https://github.com/davidderaedt/Lita). Lita's biggest drawback is its lack of error reporting when executing a SQL command, so I've also been using SQLite Run! (http://probertson.com/projects/run-air-sqlite-query-testing-tool/) because it does throw an error when you try to execute a problematic SQL statement.

SQLite Expert Personal (http://www.sqliteexpert.com/) is a much better admin tool (and it's free), but it doesn't know about Adobe's proprietary features. But if you're syncing to a server database, this probably won't matter much, if at all.

Btw, it's actually CRUD, not CURD: create, retrieve, update, delete.

I get the feeling you're looking for a "SyncLocalAndRemoteDatabases( )" function. Someone may have created something like that as part of a framework, but if not then you will have to roll up your sleeves and write some ActionScript to do this.

To start, the web server programmer creates a way for the app to send and receive updates. One way would be for this programmer to create a web service with methods (functions) for the app to call. Another would be for this programmer to create methods that use Flash Remoting.

So you have to talk to the person who is programming the web site and find out how this person plans to handle requests from the app. AFAIK Flash Remoting is the fastest and most efficient way to transfer data between a server and a Flash/AIR app -- take a look at http://www.jamesward.com/census2/. Flash Remoting transfers data using the AMF3 format, which is also an option in Flash CS. If the server programmer doesn't know Flash Remoting -- a likely scenario -- then  you might have to send and receive data as XML or JSON or name/value pairs.