Hi Hilary, welcome to the forum!
Can you kindly confirm if you have already installed the Little Reader free trial software? The *.lrp file extension you mentioned is actually a trial content file, and in order to use it you need to install the software first.
If you don't have the software yet, simply refer to this article for instructions on how to download and install the LR free trial software:
http://support.brillkids.com/index.php/article/little-reader-free-trialOnce you've installed the software, try double-clicking on the *.lrp file you downloaded earlier and this will be imported into Little Reader so you can see how the sample content works.
I hope this helps! If you're still having problems just let us know.