Let me preface this by saying I've only seen Azevedo play a handful of times, but the impression I get is that he has great hockey IQ and has really worked hard on his defensive play but seems to lack the dynamics required for a small guy to really become an NHL regular. Generally, for guys his size to become NHL players they need to be offensive dynamos or be one of the very best in a certain niche, like by being an amazing faceoff guy with great speed, an effective agitator and/or fighter and so on. Azevedo is a good player in many areas but hasn't really carved out a niche for himself since he neither a prolific scorer nor a specialized role player.
I think we will see him grind away in Manchester as a veteran a few more years and then move on.
If you asked me if he would ever play on the Kings before this year I'd have said NO. But consider that he was one of the last guys to hang around in camp this year along with King, Voinov, Loktionov and Hickey and that tells me the Kings see something in him still and he isn't considered an AHL lifer... yet. He needs to stay healthy and productive for this whole season though and he should be in pretty decent shape to win a spot in the next couple years if guys like Stoll, Rchardson, Lewis, and Cliche move on.