How can I install SQLite to be used with OpenOffice?
I think OpenOffice.org should be able to use the libsqliteodbc ODBC driver, but I have never tried it.
Edit
Okay, I tested it and will explain how to do it...
If you click the icon above to install libsqliteodbc, make sure that you also install the AddOn “Graphical tools for ODBC management and browsing (unixodbc-bin)” (so, make sure the checkbox is ticked).
Now press Alt+F2 to launch the Run application dialog window and run ODBCConfig. In the first tab "User DSN", press the "Add..." button.
You will get a "Select a driver..." dialog. Select the SQLite (version 2) or SQLite3 (version 3) driver as appropriate, then press the "Ok" button.
Now you can set up the properties for the actual ODBC Data Source. Fill in the Name field (use whatever descriptive name you want, it's there for your convenience). Fill in the Database field (use the small > button to browse & select it). Leave all the other fields alone. Press the 
button to save this Data Source.
After this you should see your new Data Source in the ODBC Data Source Administrator and in OpenOffice.org.
In OpenOffice.org select the option to connect to an existing database, select ODBC from the drop-down, then press "Next". Now you should be able to select your newly-created ODBC source when you press the "Browse" button...
You can use SQLite Manager extension for Firefox to open the database and export it as CSV,SQL or XML. I'm sure you will be able to import one of those formats into OpenOffice. However, the extension itself is enough to view and manage data inside the database. There is no need to import to OO.
If you don't want to use Firefox for that, then use a standalone application: