Awesome!!! I have a few thoughts. As far as a super-duper smaller guitar, the Taylor GS-Mini is incredibly cool. It is an instrument that sounds great, plays great, and they are well made. I am not sure, it might a little bigger than some you were looking at, but I highly suggest checking one out. It's a guitar worth keeping and playing after he has grown up. They would make a great "couch" guitar. I have almost bought one, and I have absolutely no need for it, but I just liked it.
Second thought: As much as one might not like it, he'll be growing quickly over the next few years. Getting a decent but not killer guitar may not be all bad. There are often new and used Yamaha (and similar) 3/4 size guitars available. I have set up a Yamaha with lights and low action, and it played great. You are likely going to need a little setup work done on just about any new guitar, especially inexpensive ones.
I was surprised the LXM comes with mediums, but I guess it does make sense with the shorter scale length. Going to light gauge will make a difference. It will make the strings less rigid and it will also slightly lower the action (due to less string tension). The big thing is get the action set low and perhaps it would feel great even with mediums.
Just to throw something else in there for consideration: For a super easy and fun instrument play, a Ukulele is tough to beat. A uke is very easy to fret, and learning is sped by being limited to 4 strings. The chord shapes convert over to guitar as they are tuned similar to the top four strings of a guitar (different notes, but the same relative tuning). I bought a neighbor a Makai Concert Uke for about $100 that has a solid top, and it's an absolute blast to play. I bought that one from Elderly's. I have a Baritone Uke, and the tuning on that is identical to the highest pitch four strings on a guitar. I have some nieces that are 7 and 5 and I am going to get them some concert ukes soon. I can say that starting with a uke might be the easiest way to learn something guitar-ish, but unless it's what he wants to do, it wouldn't help. If he isn't motivated to play it, it won't do anyone any good.