I only guessing but: probably you cannot manipulate the source address at that level ie HTTP::Request or LWP::UserAgent In fact due to the aim of these modules i hope they make you able to choose what IP to use to make the request if that IP is one of yours (guessing again).

I think that probably you need to make up a fake IP packet instead, perhaps using Net::RawIP

See also How can I simulate multiple IP/MAC combinations on one computer?

I'm interested in your result

L*