You have really answered your own question. Provided your script is run on an account with net access and provided your script can run within the normal CGI restrictions (server timeouts etc) then, yes, you can use LWP to get the second script from within the first.
Remember, to the OS the site is being hosted on, any CGI program is essentially just a script/program with it's output piped into another program. When you view it like that you can realise that there is little stopping you from doing anything! ;)
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