The LWP man page states:
The timeout specifies how much time we give remote servers to respond before the library disconnects and creates an internal time- out response.
However, inspecting the code and searching google and this site as well, I don't see how to detect that this internal timeout response has been created. That is, what should I replace MAGIC with in the below code: 
$response = $ua->request($r);
if (MAGIC) {
  print "timed out\n";
} elsif ($response->is_success) {
  print "yippeeeeeeeee!\n";
}

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In reply to detecting timeout in LWP by vkhera

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