I can try to prepare a suitable pull request, but will need some help to test the code - as I don't have a http proxy server to test with.
I would say that we should add a new LTI setting
$LTI_http_proxy to accept the entire "proxy value" (what was denoted as http://[proxy server]:[port]/ above), and modify the file so that when it is set the approach above will be used.
From what I found at https://metacpan.org/dist/libwww-perl/view/lwpcook.pod if the proxy requires a password a setting like
http://[user:password@proxy server]:[port]/ is supposed to work.
Is there a potential need to set a different proxy setting for http and https here? (If so, two settings will be needed.)
Since I do not think the LTI code would ever use a ftp request, so I think that there is any reason to provide a setting for ftp.