I was looking around for a decent SQLite database manager and came across an addon that works just great!

SQLite Manager by Tarakant Tripathy and Mrinal Kant
https://addons.mozilla.org/en-US/firefox/addon/5817

It supports the SQLite3 format which gives you more robust support from more data types to views and triggers.

On a related note, I was using PHP to parse some text files to be imported to the SQLite database for an Android app. I'm running PHP version 5.2 on my Mac, and I got errors when I attempted to use the sqlite library to manage the SQLite3 db. (the format that this FF addon saves)

You need to use PDO with an sqlite dsn if you want to use SQLite3 with PHP. Currently the sqlite PHP library only supports SQLite2.