Studio does not support importing LAR files from a different version. There were also some significant changes in 3.0 that would make it even more difficult to import from an earlier version.
When you upgrade Studio instance from 2.4 to 3.0, and have restored the backed-up database from 2.4, you should see your existing content, although you may need to edit or replace some components to accommodate 3.0 changes.
See the 3.0 Studio Migration Guide ("+gMapTitle+ ") for details about the changes in 3.0, including the new Studio landing page and new structure for Studio applications. The guide includes the additional steps you'll need to take for your existing pages and components.