Hi Cassandra,
You do not need to connect to the Internet to use Little Reader (whether you play or customize any lesson), although there are certain software features that will be disabled when you use LR offline. You may find a list of these particular features in the following article:
http://support.brillkids.com/index.php/article/minimum-requirements-little-readerYes, you will need to be online whenever you want to access the downloads in our Little Reader Library, but after you're done downloading the files, you do not need to stay online. Importing these files into LR will not require you to connect to the Internet.
The only time you're required to go online is during setup (in the license key activation step), because Little Reader needs to communicate with our licensing server for a few seconds to activate your copy of the software. Once you're done activating, you may disconnect and use LR without the Internet connection.
hope this helps!