Ping times will be high for some sites, but I doubt Google will be one of those. As soon as this Lunar Net goes up Google will have a server on the moon faster than you can say 'light-speed delay', so all your favourite Google services and YouTube videos will be available locally with nice low ping times. It's the rest of the internet you'll have to wait for.
I recall hearing Ted Nelson talk about his infamous Xanadu hypertext system some 20 years ago. At one point in his description, he quite seriously warned that "the system will be somewhat less responsive from the outer reaches of the solar system."<p>I gotta admit, the guy knew how to dream big.
By the time we have to worry about moon latency, I'm pretty sure all hosting companies will include a moon mirror.<p>How expensive could it be to mirror the entire internet? This is the future we're talking about.