I tried to execute local URL it is not giving me any results. I can load that private urls in browser in our corporate network but I cannot run the test against those urls.
Also I have created a local domain in my host file and tested the site with and without internet.
Running Pagespeed Insights
Pagespeed Insights: Processing results
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Strategy: desktop
Score: 66
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Number Resources | 18
Number Hosts | 5
Total Request | 1.25 kB
Number Static Resources | 16
Html Response | 14.04 kB
Css Response | 125.34 kB
Image Response | 251.87 kB
Javascript Response | 220.89 kB
Number Js Resources | 6
Number Css Resources | 3
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Avoid Landing Page Redirects | 0
Enable Gzip Compression | 19.69
Leverage Browser Caching | 7.5
Main Resource Server Response Time | 0
Minify Css | 0.12
Minify HTML | 0.12
Minify Java Script | 0
Minimize Render Blocking Resources | 20
Optimize Images | 3.06
Prioritize Visible Content | 2
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Conclusion: I believe tests are running in google server and the server cannot access my urls. Please share if you have the documentation for how tests are running. Also the urls are accessible through the browser so I don't think there is a firewall issue.