(I'm not sure about the MySQL to SQLite migration tools. As always with SQL, there are SQL dialects changes that may have to be taken into account, it really depends on your existing databases.)
MySQL and SQLite are fundamentally different in that MySQL is server-based, intended to be used by a client, whereas SQLite is file-based, intended to be used via an API that accesses the underlying files directly. As such, you don't need to manage a SQLite in the same way as you would manage MySQL, because SQLite is an embedded database. There are useful tools for connecting to SQLite databases, one of them is SQLite Manager (it doesn't have to run within Firefox).
This may be an issue for large production databases if you need concurrent access (see this SQLite FAQ.