To know more about Facebook lite installation
Is it possible to install Facebook lite in iPhone 6 with iOS 12.5.7 downloaded using safari?
You would have to ask Meta about their software, I don't know if the lite version will run on iOS 6, the full version won't. Your post is a little confusing, you either install the app on your phone or you use the web version. You don't install it through Safari.
Here is a link to their help page.