Hi there.
You will have a device SQLiteDatabase and and a remote (your computer) SQLiteDatabase.
It will be up to you to synchronise them and ensure that they remain synchronised.
How will you do that?
Has your computer got a web server running?*
If so then you can use various PHP (or other server side) functions to maintain and synchronise both databases.
BUT the process will never (or maybe!) be perfect...
If you modify the database on your computer or device then how will the other database know that a change has been made and therefore you need to synchronise both databases?
You'll need a 'last_updated' or similar column in BOTH database tables.
Now your device or computer knows when exactly the database was last updated.
Your device can send a request to your computer with a parameter 'last_updated'.
Your computer can check to see if it's data is newer than that 'last_updated' timestamp and if so return new data to your application.
You need to think about all the possible possibilities...
Has the computer version of the database been modified but the Android device database has NOT?
Or has the device database been modified and the computer version NOT?
*Your computer will need to be accessible from your device and for that you'll need to run a web server on your computer.
I'd recommend
XAMPP
Things get technical - have you any skills in PHP or other server side programmings languages?
Post again with more detail and i'll try and help.
Martin.