Is there a way to Private Message another person outside of a game that you are playing with them? I was wondering as I cannot find a way to do so.

There's not, other than creating a game with them. You can vote on this here: https://warlight.uservoice.com/forums/77051-warlight-features/suggestions/1071171-global-private-messages?ref=title

Thank you very much for both that link and the help, Fizzer.

Private messaging out of games should not be developped.
Some game creators like to unable private messaging in order to prevent alliances, if private messaging out of games is possible, then the option of disabling private messaging in-game would not make any sense anymore...

Don't you think so ?

You know, that is a good point. The reason I wanted to do so is so that I can talk to some of the people who I have played against. Maybe make it so that if you PM someone, the server checks to see if you are playing against them in a game with no private messaging or something. I will say that if Private Messaging outside of games does end up happening, then something should be done to prevent or limit that from happening. Sadly, I think that that might cause more coding for Fizzer and a little more strain on the server.