Do you know PHP or Perl, and have a web-server you can put scripts on?
If so you could code a little proxy, where the CGI queries Google with an IE or Firefox user agent. Then your Lua program will hit your cgi/php...
The only other way I know of to do this (a huge pita) is to signup for their developer API.
With a developer API, they give you an API key, and you include that as part of the search query to a special URL.
They give you 100 queries per day for free, and then you have to pay to enable more queries ($5 per 1000 extra queries)
https://developers.g...rch/v1/overview
After all that mess, you can use a URL like this:
https:// www.googleapis.com/customsearch/v1?key={INSERT-YOUR-KEY}&cx=017576662512468239146:omuauf_lfve&q={SEARCH-TERM}
They also have a JSON interface, if you wanted to go that route.