No, sorry. InLite is a database/data-management system in "one-file". This means you can not simply share this file on an online server. Therefore you have to use an server-client based database system such as mysql. If you want to create an online-database system, you should look for the mysql-include, setup an mysql-server and connect to it from the clients.
Btw., you're saying "like a real database". Since InLite isn't a "real" database, that has nothing to do with that fact. As for example, SQLite also manages the whole data in a file and is not used to share the data online, but it's a real database, anyway.
That's just how you want to use the database. In your case, you need a server-client based database, not a local one.

Regards
TSGames