I have a Martin LX. The difference is an HPL top instead of spruce. I was looking for something small for my kid to learn on. The size is great. The weight is not. The neck is a little thick, like you mentioned, but not terribly so; my kid's small hands can manage it. I think between the layered neck and the HPL, the weight of it is the biggest issue. I've heard complaints about how well the wood is glued to the HPL, but I can't speak to that. I have a Martin 0X (soprano) that I really like, which is why I gave the Martin a shot.
Would I get it again? Probably not. The sound is not that impressive, even making concessions for its size. I'm not dissatisfied, since I got a deal on it, but I'd probably make a different choice if I had to do it again. I ended up finding another deal later, on an Islander (Kanile'a) mini guitar. I didn't even know they made guitars--I don't mean their guitarlele. The Islander sounds much better, one of the best solid top laminates I've played, especially for a mini guitar. But it's bigger than the Martin. Sizing varies from maker to maker, but the Martin is more like a 1/2 size whereas the Islander is closer to a 3/4. I haven't found many guitars the size of the little Martin series.
I don't know what you're looking for in a smaller guitar, but if you want something that small for portability reasons, the weight might make you think twice; the Martin feels like a full size guitar. The spruce top on the LX1 instead of the HPL top might make it a bit lighter, but the neck adds much of the weight.
My kid's small and the size of the Martin works for her now. But I have the Islander for her to move on to when she gets a little bigger. The Islander, if you're interested in that as an option, was about $100 more than the Martin, but it's larger size might not make it as good for travel.