One thing that kept Lord of the Rings from being the perfect solo game for me was that the board could get convoluted really fast. This was especially true when playing two-handed, i.e. controlling two decks at the same time. Often, mundane choices could take forever, just because of the sheer number of cards involved. It didn't help at all that there was no hand size limit, and card draw was abundant.
Overall, I think that the game suffered, because the designers didn't control how much stuff could be in play and in player's hands at the same time. Game of Thrones comes to my mind as an example of how to approach this correctly: there are many effects and mechanisms that remove cards from the board and from players hands throughout the game, so that clutter is rarely an issue.
What is your experience with Arkham Horror so far? Judging by the rules alone, it seems that cards don't tend to 'pile up' as much as they do in Lord of the Rings. I would be really excited for a solo LCG that requires you to make difficult choices rather than keeping track of a huge board state. Here in Germany we unfortunately have to wait until next year for the localization of the game, but in the meantime I would like to hear the opinions of some of you lucky people who already played it.