I think writing to improve reading is a great idea (though take that with a grain of salt -- I am someone who really enjoys writing) --
I don't think a writing class is necessary just to study for the LSAT (though you may want to take a writing class for other reasons). You should take an LSAT class to study for the LSAT!
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You may, though, just want to try writing out some LSAT-like passages yourself --
Sorry to be so specific, but here's a scenario that I think could be useful:
Imagine a debate between two ideas / arguments etc --
could be cats are better pets vs dogs are better pets
could be who's better between two contestants on american idol
could be some argument between two people in your family
Now, imagine you have to write a three or four paragraph essay about this. You're going to give reasons for both sides (and vary it up - sometimes 50%, 50% each side , 90%, 10% other times). And- here's the kicker -- as the author, you're going to put in some subtle hints about which side you think is right, but you won't ever use the the first person (I, me, my, etc). Try to be as subtle as you possibly can.
I think if you try to carefully craft two or three versions of the above, it could help you much more easily spot the structure of LSAT passages. It'll help you see them as (generally) opposing ideas, with opinions and reasons given for both sides -- most importantly the author's opinion often subtly on one side or the other -- and if you can do this, it will improve your reading speed, and your accuracy with the questions, a great deal.
Hope that is helpful!