Oh, look, Season 3 of VLD had *SPOILER ALERT* a whole episode dealing with an alternate reality with EVIL ALTEANS AND A BRAIN CONTROLLED SOCIETY.
Guys, I have never brainstormed and written out a one-shot so fast in my entire life. :-)
In brief: I picture the Paladins of Voltron (yes, all of them) existing in that reality as well, but Keith is really persona-non-grata for being, you guessed it, Galra.
Basically any more setup is...kind of non-existent. Basically I just /really/ wanted to write the team going in to rescue Keith and I really liked the non-cog aspect of that episode, so the general setup should explain itself as you read the story.
Latest update: I promise, I am still working on another story for 'Lost Paladins' - but I've been working through a lot lately. I go more into it on my Tumblr (same name as here, Rangergirl3), so if you're interested in keeping up to date on stuff that I write, that's the best place to find it! :-)