Hi James,
The default configuration should work for the lite version as well. I’m guessing there might be javascript related issue or something similar there. The screenshot looks fine to me.
Also, make sure the Google analytics pageview string for the lite version is:
[html]?ajax_search={asl_term}[/html]
Screenshot: http://i.imgur.com/P94xjCb.png
Note that there is one character difference in that string from the Pro version. (the string is asl_term in the lite version instead of asp_term)
If that sits as well, there might be a different problem. If you can, please link the page here and I will take a look.