What LWP::UserAgent sends is perfectly valid and also perfectly common.

Personally, I would investigate what the server thinks it is receiving. See RFC 7230, section 5.3 on how the line could be formatted.

Also, in your case, I would investigate whether you're connecting to an HTTP proxy (which needs the full HTTP URL) instead of a HTTP server. In that case, maybe you did not set $ENV{HTTP_PROXY} or LWP::UserAgent picked up the wrong variables for that.