That's just where the practice comes in. On the logic games you'll have maybe 7 to 10 entities at the very most, and you'll probably have to order them in some manner in an equivalent number of slots.
Once you work through a few of them, your brain gets much better at recognizing patterns and relationships, and the "chunks" with which you analyze grow larger and more useful.
I've seen your performance in that math problems thread. You wouldn't have any trouble.
Someone who sees this: Find the sum of 1+2+3+4+5...+1,000,000 might have no idea what to do. Someone accustomed to mathematics, though, would immediately suspect the existence of certain patterns, would experiment a little to find them, perhaps write out a couple of equations expressing what we do know, and would in short order come up with an equation to give us the desired answer.
Same thing with those logic games. Your brain just has to become accustomed to the type of data and connections.
Other analogies... chess problems become progressively easier to do and visualize the more familiar one becomes with the board and patterns. What seems at first like an immense and unwieldy amount of information soon reduces itself in the mind to very usable chunks of information.
Someone watching a football game doesn't see 22 unique entities running on a field; he sees a quarterback, the ball, the likely objectives of the offense, of the defense, the efforts of some to tackle the QB, etc. And he chunks the data he sees as well: there is the structure of the line, the number of receivers, the actions in the backfield, etc.
G. Polya, in his works on heuristics, liked to talk of the importance of looking back over a solved problem until one can see it all "at a glance." And I think the essence of that is learning to chunk the information appropriately and just see the connections.
First brushes with a new type of problem always involve a certain amount of normalization. When you took that LSAT, you were forcing yourself to normalize to the new type under sharp time constraints, which isn't optimal. It's also not indicative, necessarily, of how much you'd be able to learn.
