This is in the documentation for
LWP::Simple:
The user agent created by this module will identify itself
as "LWP::Simple/#.##" (where "#.##" is the libwww-perl
version number) and will initialize its proxy defaults
from the environment (by calling $ua->env_proxy).
and for
LWP::UserEgent:
$ua->env_proxy
Load proxy settings from *_proxy environment variables. You might specify proxies like this (sh-syntax):
gopher_proxy=http://proxy.my.place/
wais_proxy=http://proxy.my.place/
no_proxy="localhost,my.domain"
export gopher_proxy wais_proxy no_proxy
csh or tcsh users should use the "setenv" command to
define these environment variables.
On systems with case insensitive environment variables
there exists a name clash between the CGI environment
variables and the "HTTP_PROXY" environment variable
normally picked up by env_proxy(). Because of this
"HTTP_PROXY" is not honored for CGI scripts. The
"CGI_HTTP_PROXY" environment variable can be used
instead.
So you should be able to simply set the appropriate environment variables.