How to install mod_pagespeed on Apache Server on Mac?
mod_pagespeedis currently not supported. However, you can build it from source. Google is describing here how you can do that. 

Instead of using apt-get you can install brew. Brew is a lightweight package manager for OS X and can be obtained at their official homepage.

I'd recommend to install a Linux distro on a VM and then installing mod_pagespeed as this is way easier, plus you get more support probably.