Of course you can.

Actually, there are two ways. The first one is to simply export the saves to the full version. Just start the lite after the full version has been installed, and there will be a "Transfer saves to The Quest" menu point on the main menu.
The second way is to use iTunes File Sharing and copy the saves from the lite to your computer, then copy them from the computer to the full version (see the "Transfer save games from iPhone to iPad" topic in this very forum for details).