Following this post, outgoing traffic will go through the proxy only if the requesting app knows the proxy url, if it doesn't then sending the request out of the LAN is denied by the proxy.
In this case it's like the app saying to the LAN "I'd like to get this from the web", and the LAN's proxy answering "No, you didn't say Simon Says".
Why is the proxy acting like this instead of just intercepting the request, doing necessary security check, and sending the request to the outside ?
And, obviously the LAN knows the proxy url, then why the need for the app to specify it when it wants to send HTTP requests outside the LAN ?