Q: I use OS X 10.7.5, I get the message: "Software Update can't check for updates because of a network problem" yet I run diagnostics and it says everything is working proerly.  How do I update?

Well if your running your web browser and can get around to websites, then it's not a Mac or local network issue, but something is wrong with Apple or Akamai servers which host the OS X updates.

You'll just have to wait it out.

Your on 10.7.5, that's the latest update for OS X.

Are you running Safari 6.0.1? That was the latest Software Update for 10.7.5 users.

https://support.apple.com/kb/HT1222

Have you tried AppStore?, I think Apple is running the updates through there to rope users into that enviroment for the eventual closing of the platform to software from outside sources.